2,267 results
Search Results
2. On sentinel method of one-phase Stefan problem.
- Author
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Merabti, Nesrine Lamya, Batiha, Iqbal M., Rezzoug, Imad, Ouannas, Adel, and Ouassaeif, Taki-Eddine
- Subjects
- *
SOLID-liquid interfaces , *NUMERICAL analysis , *NONLINEAR analysis , *APPROXIMATION theory , *UNIQUENESS (Mathematics) - Abstract
This paper is interested in studying the one-phase Stefan problem. For this purpose, we use the nonlinear sentinel method, which relies typically on the approximate controllability and the Fanchel-Rockafellar duality of the minimization problem, to prove the existence and uniqueness of a solution to this problem. In particular, our research focuses on the application of the nonlinear sentinel method to the single-phase Stefan problem. This approach aids in identifying an unspecified boundary section within the domain undergoing a liquid-solid phase transition. We track the evolution of the temperature profile in the liquid-solid material and the corresponding movement of its interface over time. Eventually, the local convergence used for the iterative numerical scheme is demonstrated. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. NEW MEDIAN BASED ALMOST UNBIASED EXPONENTIAL TYPE RATIO ESTIMATORS IN THE ABSENCE OF AUXILIARY VARIABLE.
- Author
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HUSSAIN, SAJAD and BHAT, VILAYAT ALI
- Subjects
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MEDIAN (Mathematics) , *APPROXIMATION theory , *NUMERICAL analysis - Abstract
The problem of biasness and availability of auxiliary variable for the estimating population mean is a big concern, both can be handled by proposing unbiased estimators in the absence of auxiliary variable. So in this paper unbiased exponential type estimators of population mean have been proposed. The estimators are proposed in the absence of the instrumental variable called the auxiliary variable by taking the advantage of the population and the sample median of the study variable. To about the first order approximation, the theoretical formulations of the bias and mean square error (MSE) are obtained. The circumstances in which the suggested estimators have the lowest mean squared error values when compared to the existing estimators were also deduced. In comparison to the currently used estimators, it was discovered that the suggested estimators of population mean had the lowest MSE, hence highest efficiency. Also least influence from the data's influential observations when it came to accurately calculating the population mean for skewed data. The theoretical findings of the paper are validated by the numerical study. [ABSTRACT FROM AUTHOR]
- Published
- 2023
4. ONIC B-SPLINE APPROACH FOR ADVECTION DIFFUSION EQUATION.
- Author
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KIRLI, Emre
- Subjects
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ADVECTION-diffusion equations , *DISCRETIZATION methods , *APPROXIMATION theory , *NUMERICAL analysis , *COLLOCATION methods - Abstract
In this paper, a highly accurate method is introduced to achieve the numerical solution of the advection diffusion equation (ADE). This approach contains collocation technique based on nonic B-spline functions in the spatial-domain discretization and Adams Moulton scheme in the temporal-domain discretization. Two test problems are studied to validate effectiveness of the new presented method and efficiency of the approximate results are tested by calculating rate of temporal-convergence and error norm L8 for the suggested method. The obtained numerical results are compared in the tables by the other available studies in literature and it is observed that a better approximate solution is provided than the existing methods. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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5. On some properties of linear functionals.
- Author
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Stefanov, Stefan M.
- Subjects
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MATHEMATICAL optimization , *APPROXIMATION theory , *NUMERICAL analysis , *VECTOR spaces , *LINEAR operators , *FUNCTIONALS , *FUNCTIONAL analysis - Abstract
In this paper, some properties of linear functionals are studied, which are used in functional analysis, optimization theory, numerical analysis, approximation theory, various applications, etc. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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6. Iterative Approach for a Class of Fuzzy Volterra Integral Equations Using Block Pulse Functions.
- Author
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Zakeri, K. Akhavan, Araghi, M. A. Fariborzi, and Ziari, S.
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INTEGRAL equations , *APPROXIMATION theory , *LIPSCHITZ spaces , *NUMERICAL analysis , *NONLINEAR analysis - Abstract
Fuzzy Integral equations is a mathematical tool for modeling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equations (NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented approach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is provided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered. [ABSTRACT FROM AUTHOR]
- Published
- 2022
7. Correlation energy extrapolation by intrinsic scaling. II. The water and the nitrogen molecule.
- Author
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Bytautas, Laimutis and Ruedenberg, Klaus
- Subjects
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NUMERICAL analysis , *APPROXIMATION theory , *PERTURBATION theory , *MOLECULES , *EXTRAPOLATION , *ASYMPTOTIC expansions - Abstract
The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H2O and N2. As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configuration-interaction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]
- Published
- 2004
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8. Biased diffusion in tubes of alternating diameter: Numerical study over a wide range of biasing force.
- Author
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Makhnovskii, Yurii A., Berezhkovskii, Alexander M., Antipov, Anatoly E., and Zitserman, Vladimir Yu.
- Subjects
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DIFFUSION , *DIAMETER , *NUMERICAL analysis , *PARAMETER estimation , *APPROXIMATION theory , *INTERMEDIATES (Chemistry) - Abstract
This paper is devoted to particle transport in a tube formed by alternating wide and narrow sections, in the presence of an external biasing force. The focus is on the effective transport coefficients--mobility and diffusivity, as functions of the biasing force and the geometric parameters of the tube. Dependences of the effective mobility and diffusivity on the tube geometric parameters are known in the limiting cases of no bias and strong bias. The approximations used to obtain these results are inapplicable at intermediate values of the biasing force. To bridge the two limits Brownian dynamics simulations were run to determine the transport coefficients at intermediate values of the force. The simulations were performed for a representative set of tube geometries over a wide range of the biasing force. They revealed that there is a range of the narrow section length, where the force dependence of the mobility has a maximum. In contrast, the diffusivity is a monotonically increasing function of the force. A simple formula is proposed, which reduces to the known dependences of the diffusivity on the tube geometric parameters in both limits of zero and strong bias. At intermediate values of the biasing force, the formula catches the diffusivity dependence on the narrow section length, if the radius of these sections is not too small. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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9. Fitting high-dimensional potential energy surface using active subspace and tensor train (AS+TT) method.
- Author
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Baranov, Vitaly and Oseledets, Ivan
- Subjects
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POTENTIAL energy surfaces , *TENSOR algebra , *APPROXIMATION theory , *NUMERICAL analysis , *MOLECULAR conformation , *NITROUS acid - Abstract
This paper is the first application of the tensor-train (TT) cross approximation procedure for potential energy surface fitting. In order to reduce the complexity, we combine the TT-approach with another technique recently introduced in the field of numerical analysis: an affine transformation of Cartesian coordinates into the active subspaces where the PES function has the most variability. The numerical experiments for the water molecule and for the nitrous acid molecule confirm the efficiency of this approach. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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10. A C0 virtual element method for the biharmonic eigenvalue problem.
- Author
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Meng, Jian and Mei, Liquan
- Subjects
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EIGENVALUES , *APPROXIMATION theory , *SPECTRAL theory , *BIHARMONIC equations , *NUMERICAL analysis , *FUNCTIONAL analysis - Abstract
From the eigenvalue problem theory, we see that the convergence rate of the biharmonic eigenvalues obtained by the mixed method in I. Bab u ˇ ska and J. Osborn, [Eigenvalue Problems, Handbook of Numerical Analysis, Vol. II, North-Holland, Amsterdam, 1991.] is h 2 k − 2 for k ≥ 2. In this paper, we give a presentation of the lowest-order virtual element method for the approximation of Kirchhoff plate vibration problem. This discrete scheme is based on a conforming H 1 (Ω) × H 1 (Ω) formulation, following the variational formulation of Ciarlet–Raviart method, which allows us to make use of simpler and lower-regularity virtual element space. By using the classical spectral approximation theory in functional analysis, we prove the spectral approximation and optimal convergence order h 2 for the eigenvalues. Finally, some numerical experiments are presented, which show that the proposed numerical scheme can achieve the optimal convergence order. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
11. Numerical approach for the calendering process using Carreau-Yasuda fluid model.
- Author
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Javed, Muhammad Asif, Ali, Nasir, Arshad, Sabeen, and Shamshad, Shahbaz
- Subjects
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FLUID dynamics , *APPROXIMATION theory , *COMPUTER algorithms , *NUMERICAL analysis - Abstract
This paper presents a numerical study of the calendering mechanism. The calendered material is represented using the Carreau-Yasuda fluid model. The governing flow equations in the calendering process are made first dimensionless then the lubrication approximation theory (LAT) is used to simplify them. The simplified flow equations are transformed into stream function and then are numerically solved. A numerical method is constructed with Matlab's built-in-bvp4c routine to find the stream function and pressure gradient. We use the Runge-Kutta algorithm to calculate the pressure and mechanical quantities related to the calendering process. In this analysis the pressure distribution increases with increasing Weissenberg number, however the pressure domain length decreases as the Weissenberg number increases. The pressure inside the nip region decreases from its Newtonian value when the power law index is less than one (shear thinning), and the pressure profile increases from its Newtonian pressure when the power law index is greater than one(shear thickening). How the Carreau-Yasuda fluid model parameters influence the velocity and related calendering process quantities are also discussed via graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
12. Caputo's Finite Difference Solution of Fractional Two-Point Boundary Value Problems Using SOR Iteration.
- Author
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Rahman, R., Ali, N. A. M., Sulaiman, J., and Muhiddin, F. A.
- Subjects
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FINITE difference method , *CAPUTO fractional derivatives , *BOUNDARY value problems , *APPROXIMATION theory , *NUMERICAL analysis - Abstract
The aim of this paper deals with Caputo's solution of fractional two-point boundary value problems by using second-order central difference discretization scheme and Caputo's fractional operator to construct a Caputo's finite differences approximation equation. Then this approximation equation was be used to generate a linear system. In this paper, the Successive Over-Relaxation (SOR) method has been considered as linear solver. To do this matter, this method is derive based on the Caputo's approximation equation. Based on numerical results, solutions in this problem will show SOR method is requires less amount of number of iterations and computational time as compared with GS method. In term of number of iterations, performance analysis of SOR methods has drastically decreased between 95.00% and 99.99% with the execution time decline between 87.00% and 99.99% respectively as compared with GS method. The numerical result showed that the SOR method is more efficient as compared with GS method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
13. Efficient computational analysis of non-exhaustive service vacation queues: BMAP/R/1/N(∞) under gated-limited discipline.
- Author
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Banik, A.D. and Ghosh, Souvik
- Subjects
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MARKOV processes , *MATHEMATICAL variables , *NUMERICAL analysis , *APPROXIMATION theory , *FINITE element method - Abstract
Highlights • A finite-buffer vacation queue with batch Markovian arrival process has been analyzed. • The server is subjected to serve under gated-limited service discipline. • Proposed analysis is based on the successive substitution and the supplementary variable method. • The results have been matched with the corresponding infinite-buffer queue. • Numerical results are presented for different service- and vacation-time distributions. Abstract This paper analyzes the finite-buffer single server queue with vacation(s). It is assumed that the arrivals follow a batch Markovian arrival process (BMAP) and the server serves customers according to a non-exhaustive type gated-limited service discipline. It has been also considered that the service and vacation distributions possess rational Laplace-Stieltjes transformation (LST) as these types of distributions may approximate many other distributions appeared in queueing literature. Among several batch acceptance/rejection strategies, the partial batch acceptance strategy is discussed in this paper. The service limit L (1 ≤ L ≤ N) is considered to be fixed, where N is the buffer-capacity excluding the one in service. It is assumed that in each busy period the server continues to serve until either L customers out of those that were waiting at the start of the busy period are served or the queue empties, whichever occurs first. The queue-length distribution at vacation termination/service completion epochs is determined by solving a set of linear simultaneous equations. The successive substitution method is used in the steady-state equations embedded at vacation termination/service completion epochs. The distribution of the queue-length at an arbitrary epoch has been obtained using the supplementary variable technique. The queue-length distributions at pre-arrival and post-departure epoch are also obtained. The results of the corresponding infinite-buffer queueing model have been analyzed briefly and matched with the previous model. Net profit function per unit of time is derived and an optimal service limit and buffer-capacity are obtained from a maximal expected profit. Some numerical results are presented in tabular and graphical forms. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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14. Generalized conditioning based approaches to computing confidence intervals for solutions to stochastic variational inequalities.
- Author
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Lamm, Michael and Lu, Shu
- Subjects
- *
NUMERICAL analysis , *APPROXIMATION theory , *STOCHASTIC convergence , *VARIATIONAL inequalities (Mathematics) , *SAMPLE average approximation method - Abstract
Stochastic variational inequalities (SVI) provide a unified framework for the study of a general class of nonlinear optimization and Nash-type equilibrium problems with uncertain model data. Often the true solution to an SVI cannot be found directly and must be approximated. This paper considers the use of a sample average approximation (SAA), and proposes a new method to compute confidence intervals for individual components of the true SVI solution based on the asymptotic distribution of SAA solutions. We estimate the asymptotic distribution based on one SAA solution instead of generating multiple SAA solutions, and can handle inequality constraints without requiring the strict complementarity condition in the standard nonlinear programming setting. The method in this paper uses the confidence regions to guide the selection of a single piece of a piecewise linear function that governs the asymptotic distribution of SAA solutions, and does not rely on convergence rates of the SAA solutions in probability. It also provides options to control the computation procedure and investigate effects of certain key estimates on the intervals. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
15. KERNEL-BASED DISCRETIZATION FOR SOLVING MATRIX-VALUED PDEs.
- Author
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GIESL, PETER and WENDLAND, HOLGER
- Subjects
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DIFFERENTIAL equations , *NUMERICAL analysis , *MATHEMATICAL analysis , *APPROXIMATION theory , *KERNEL functions - Abstract
In this paper, we discuss the numerical solution of certain matrix-valued PDEs. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop and analyze a new meshfree discretization scheme using kernel-based approximation spaces. However, since these approximation spaces have now to be matrix-valued, the kernels we need to use are fourth-order tensors. We will review and extend recent results on even more general reproducing kernel Hilbert spaces. We will then apply this general theory to solve a matrix-valued PDE and derive error estimates for the approximate solution. The paper ends with applications to typical examples from dynamical systems. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
16. Numerical simulations of nonlocal phase-field and hyperbolic nonlocal phase-field models via localized radial basis functions-based pseudo-spectral method (LRBF-PSM).
- Author
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Zhao, Wei, Hon, Y.C., and Stoll, Martin
- Subjects
- *
RADIAL basis functions , *DISCRETIZATION methods , *APPROXIMATION theory , *COLLOCATION methods , *NUMERICAL analysis - Abstract
In this paper we consider the two-dimensional nonlocal phase-field and hyperbolic nonlocal phase-field models to obtain their numerical solutions. For this purpose, we propose a localized method based on radial basis functions (RBFs), namely localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for spatial discretization. The basic idea of the LRBF-PSM is to construct a set of orthogonal functions by RBFs on each overlapping sub-domain from which the global solution can be obtained by extending the approximation on each sub-domain to the entire domain. This approach does not require meshing in spatial domain and hence inherits the meshless and spectral convergence properties of the global radial basis functions collocation method (GRBFCM). Some numerical results indicate that the obtained simulations via the LRBF-PSM is effective and stable for approximating the solution of nonlocal models investigated in the current paper. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
17. Numerical study of fractional quadratic Riccati differential equation using Padé approximation.
- Author
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Turut, Veyis
- Subjects
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DIFFERENTIAL equations , *APPROXIMATION theory , *POWER series , *UNIVARIATE analysis , *NUMERICAL analysis - Abstract
In this paper, univariate Padé approximation is applied to fractional power series solutions of fractional quadratic Riccati differential equation.. As it is seen from the tables, univariate Padé approximation gives reliable solutions and numerical results. [ABSTRACT FROM AUTHOR]
- Published
- 2021
18. What`s the Utility of the Case-Study Method for Social Science Research? A Response to Critiques from the Qualitative/Statistical Perspective.
- Author
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Chima, Jugdep S.
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SOCIAL science research , *METHODOLOGY , *NUMERICAL analysis , *APPROXIMATION theory , *RESEARCH - Abstract
This paper argues that the discipline's near rejection of the case-study method is based on a restrictive view of the social sciences. Critiques of the case-study method are usually predicated on the assumption that the primary task of social science research is theory-testing (hypothesis-testing). In contrast, I demonstrate the utility of the case-study method for theory-building and theory-elaboration (or theory-reconstruction). I also answer the critics' two main criticisms of the case-study methd- the lack of "internal validity" and the lack of "external validity." The paper argues that the first criticism is only valid if the explicit purpose of analysis is the formal testing of causal relationships or hypotheses. I argue that the "internal validity" of case-study findings is predicated on the plausibility of analysis, the logical nexus between the independent and dependent variables, and the explantory utility of the findings. The second main criticism- the lack of "external validity"- is only valid if the explicit purpose of the research is enumerative extrapolation from a statistical sample to a parent universe. I argue that another purpose of social inquiry is analytical extrapolation by which causal processes occurring within one case are used to explain a particular social phenomenon, and also reevaluate theories about the general phenomenon in question. The "quasi-judicial" method and collegial review are ways to determine both "internal" and "external" validity. ..PAT.-Conference Proceeding [ABSTRACT FROM AUTHOR]
- Published
- 2005
19. Multivalue-multistage Method for Second-order ODEs.
- Author
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Ismail, Ainathon and Rabiei, Faranak
- Subjects
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DIFFERENTIAL equations , *ALGORITHMS , *NUMERICAL analysis , *VECTOR analysis , *APPROXIMATION theory - Abstract
The aim of this paper is to generate the needed framework to develop order conditions for second-order Ordinary Differential Equations (ODEs) by class of multivalue-multistage Nystrom method. A general approach to study the order conditions of the methods for solving second-order initial value problems is investigated. Our investigation will be carried out by adapting the theory of Nystrom-series and using the sets of second order rooted trees for solving second-order ODEs which leads to a general set of order conditions. In this paper the method of order three using constant step-size algorithm is derived. The stability region of method is also proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
20. Numerical Methods on European Option Second Order Asymptotic Expansions for MultiScale Stochastic Volatility.
- Author
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Canhanga, Betuel, Ying Ni, Rančić, Milica, Malyarenko, Anatoliy, and Silvestrov, Sergei
- Subjects
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NUMERICAL analysis , *ASYMPTOTES , *STOCHASTIC analysis , *FOURIER transforms , *LAPLACE transformation , *APPROXIMATION theory - Abstract
After Black-Scholes proposed a model for pricing European Options in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption made by Black-Scholes was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced stochastic volatilities to the asset dynamic modeling. In 2009, Christo ersen empirically showed "why multifactor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christo ersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented a semi-analytical formula to compute an approximate price for American options. The huge calculation involved in the Chiarella and Ziveyi approach motivated the authors of this paper in 2014 to investigate another methodology to compute European Option prices on a Christo ersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present paper we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
21. A PRACTICAL USE OF RADIAL BASIS FUNCTIONS INTERPOLATION AND APPROXIMATION.
- Author
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Škala, Vaclav
- Subjects
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RADIAL basis functions , *APPROXIMATION theory , *INTERPOLATION , *MATHEMATICS , *MESHFREE methods , *NUMERICAL analysis - Abstract
Interpolation and approximation methods are used across many fields. Standard interpolation and approximation methods rely on "ordering" that actually means tessellation in d-dimensional space in general, like sorting, triangulation, generating of tetrahedral meshes etc. Tessellation algorithms are quite complex in d-dimensional case. On the other hand, interpolation and approximation can be made using meshfree (meshless) techniques using Radial Basis Function (RBF). The RBF interpolation and approximation methods lead generally to a solution of linear system of equations. However, a similar approach can be taken for a reconstruction of a surface of scanned objects, etc. In this case this leads to a linear system of homogeneous equations, when a different approach has to be taken. In this paper we describe novel approaches based on RBFs for data interpolation and approximation generally in d-dimensional space. We will show properties and differences of "global" and "Compactly Supported RBF (CSRBF)", run-time and memory complexities. As the RBF interpolation and approximation naturally offer smoothness, we will analyze such properties as well as approaches how to decrease computational expenses. The proposed meshless interpolation and approximation will be demonstrated on different problems, e.g. in painting removal, restoration of corrupted images with high percentage of corrupted pixels, digital terrain interpolation and approximation for GIS applications and methods for decreasing computational complexity. [ABSTRACT FROM AUTHOR]
- Published
- 2016
22. Multi-scale perimeter control approach in a connected-vehicle environment.
- Author
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Yang, Kaidi, Zheng, Nan, and Menendez, Monica
- Subjects
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PERIMETERS (Geometry) , *APPROXIMATION theory , *NUMERICAL analysis , *PREDICTIVE control systems , *PERFORMANCE evaluation - Abstract
This paper proposes a novel approach to integrate optimal control of perimeter intersections (i.e. to minimize local delay) into the perimeter control scheme (i.e. to optimize traffic performance at the network level). This is a complex control problem rarely explored in the literature. In particular, modeling the interaction between the network level control and the local level control has not been fully considered. Utilizing the Macroscopic Fundamental Diagram (MFD) as the traffic performance indicator, we formulate a dynamic system model, and design a Model Predictive Control (MPC) based controller coupling two competing control objectives and optimizing the performance at the local and the network level as a whole. To solve this highly non-linear optimization problem, we employ an approximation framework, enabling the optimal solution of this large-scale problem to be feasible and efficient. Numerical analysis shows that by applying the proposed controller, the protected network can operate around the desired state as expressed by the MFD, while the total delay at the perimeter is minimized as well. Moreover, the paper sheds light on the robustness of the proposed controller. This multi-scale hybrid controller is further extended to a stochastic MPC scheme, where connected vehicles (CV) serve as the only data source. Hence, low penetration rates of CVs lead to strong noises in the controller. This is a first attempt to develop a network-level traffic control methodology by using the emerging CV technology. We consider the stochasticity in traffic state estimation and the shape of the MFD. Simulation analysis demonstrates the robustness of the proposed stochastic controller, showing that efficient controllers can indeed be designed with this newly-spread vehicle technology even in the absence of other data collection schemes (e.g. loop detectors). [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
23. Generation and application of multivariate polynomial quadrature rules.
- Author
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Jakeman, John D. and Narayan, Akil
- Subjects
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MULTIVARIATE analysis , *SCIENTIFIC computing , *APPROXIMATION theory , *NUMERICAL analysis , *MONTE Carlo method - Abstract
The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many aspects of scientific computing with complex models. The contribution of this paper is twofold. First, we provide novel mathematical analysis of the polynomial quadrature problem that provides a lower bound for the minimal possible number of nodes in a polynomial rule with specified accuracy. We give concrete but simplistic multivariate examples where a minimal quadrature rule can be designed that achieves this lower bound, along with situations that showcase when it is not possible to achieve this lower bound. Our second contribution is the formulation of an algorithm that is able to efficiently generate multivariate quadrature rules with positive weights on non-tensorial domains. Our tests show success of this procedure in up to 20 dimensions. We test our method on applications to dimension reduction and chemical kinetics problems, including comparisons against popular alternatives such as sparse grids, Monte Carlo and quasi Monte Carlo sequences, and Stroud rules. The quadrature rules computed in this paper outperform these alternatives in almost all scenarios. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
24. Extended Semismooth Newton Method for Functions with Values in a Cone.
- Author
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Bernard, Séverine, Cabuzel, Catherine, Nuiro, Silvère Paul, and Pietrus, Alain
- Subjects
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BANACH spaces , *NUMERICAL analysis , *FUNCTIONAL equations , *MATHEMATICAL functions , *APPROXIMATION theory - Abstract
This paper deals with variational inclusions of the form 0∈K−f(x)
where f:Rn→Rm is a semismooth function and K is a nonempty closed convex cone in Rm . We show that the previous problem can be solved by a Newton-type method using the Clarke generalized Jacobian of f . The results obtained in this paper extend those obtained by Robinson in the famous paper (Robinson in Numer. Math. 19:341-347, 1972 ). We provide a semilocal method with a superlinear convergence that is new in the context of semismooth functions. Finally, numerical results are also given to illustrate the convergence. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
25. Dynamic discrete models for the granular matter formation process.
- Author
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Khapalov, Alexander and Lapin, Sergey
- Subjects
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DISCRETE systems , *PARTIAL differential equations , *APPROXIMATION theory , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
In this paper, we introduce a new modelling approach for the dynamic granular matter formation process in the form of a system of difference equations, directly tailored to the physical nature of the process at hand. Respectively, the dynamic 1D and 2D discrete models, proposed in this paper, are not constructed as numerical schemes approximating some partial differential equations (PDEs).We propose here to look for the functions describing the standing and the rolling layers of the granular matter as the limits of discrete solutions to the aforementioned model equations as the size of the mesh tends to zero. In particular, this approach allows us to differentiate between the influx of the rolling layer coming down from different directions to the corner points of the standing layer. Such points are difficult to adequately describe by means of PDEs and their straightforward numerical approximations, typically 'ignoring' the system's behaviour on the sets of zero measure. However, these points are critical for understanding the dynamics of formation process when the standing layer is created by the moving front of the rolling matter or when the latter is filling a cavity and/or stops rolling. The existence of distributed (infinite-dimensional) limit solutions to our discrete models as the size of the mesh tends to zero is also discussed. We illustrate our findings by numerical examples which use our models as the direct algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
26. Numerical methods for Stochastic differential equations: two examples.
- Author
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Carassus, Laurence, Darbas, Marion, Gayraud, Ghislaine, Goubet, Olivier, Salmon, Stéphanie, de Raynal, Paul-Éric Chaudru, Pagès, Gilles, and Rey, Clément
- Subjects
- *
STOCHASTIC difference equations , *NUMERICAL analysis , *APPROXIMATION theory , *LANGEVIN equations , *MONTE Carlo method - Abstract
The goal of this paper is to present a series of recent contributions arising in numerical probability. First we present a contribution to a recently introduced problem: stochastic differential equations with constraints in law, investigated through various theoretical and numerical viewpoints. Such a problem may appear as an extension of the famous Skorokhod problem. Then a generic method to approximate in a weak way the invariant distribution of an ergodic Feller process by a Langevin Monte Carlo simulation. It is an extension of a method originally developed for diffusions and based on the weighted empirical measure of an Euler scheme with decreasing step. Finally, we mention without details a recent development of a multilevel Langevin Monte Carlo simulation method for this type of problem. [ABSTRACT FROM AUTHOR]
- Published
- 2018
27. Nonconservative hyperbolic systems in fluid mechanics.
- Author
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Carassus, Laurence, Darbas, Marion, Gayraud, Ghislaine, Goubet, Olivier, Salmon, Stéphanie, Aregba-Driollet, Denise, Brull, Stéphane, and Lhébrard, Xavier
- Subjects
- *
FLUID mechanics , *HYPERBOLIC spaces , *DISCRETIZATION methods , *APPROXIMATION theory , *NUMERICAL analysis - Abstract
This paper is devoted to the numerical approximation of nonconservative hyperbolic systems. More precisely, we consider the bitemperature Euler system and we propose two methods of discretization. The first one is a kinetic approach based on an underlying kinetic model. The second one deals with a Suliciu approach when magnetic fields are taken into account. [ABSTRACT FROM AUTHOR]
- Published
- 2018
28. Renormalization of the frozen Gaussian approximation to the quantum propagator.
- Author
-
Tatchen, Jörg, Pollak, Eli, Tao, Guohua, and Miller, William H.
- Subjects
- *
RENORMALIZATION (Physics) , *GAUSSIAN processes , *APPROXIMATION theory , *QUANTUM theory , *DEGREES of freedom , *FORCE & energy , *NUMERICAL analysis , *OSCILLATIONS - Abstract
The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining 'on the fly' quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to 'on the fly' computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable 'on the fly'; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
29. Error analysis of molecular dynamics and fractal time approximants from a combinatorial perspective.
- Author
-
Paul, Reginald
- Subjects
- *
ERROR analysis in mathematics , *MOLECULAR dynamics , *APPROXIMATION theory , *COMBINATORICS , *BOUNDARY value problems , *THERMODYNAMICS , *NUMERICAL analysis , *SIMULATION methods & models - Abstract
Trotter's theorem forms the theoretical basis of most modern molecular dynamics. In essence this theorem states that a time displacement operator (a Lie operator) constructed by exponentiating a sum of noncommuting operators can be approximated by a product of single operators provided the time interval is 'very small.' In theory 'very small' implies infinitesimally small (at which point the approximate product becomes exact), while in practical analysis a finite time interval is divided into several small subintervals or steps. It follows, therefore, that the larger the number of steps the better the approximation to the exact time displacement operator. The question therefore arises: How many steps are sufficient? For bounded operators, standard theorems are available to provide the answer. In this paper we show that a very simple combinatorial formula can be derived which allows the computation of the global differences (as a function of the number of steps) between the Taylor coefficients of the exact time displacement operator and an approximate one constructed by using a finite number of steps. The formula holds for both bounded and nonbounded operators and shows, quantitatively, what is qualitatively expected-that the error decreases with increasing number of steps. Furthermore, the formula applies irrespective of the complexity of the system, boundary conditions, or the thermodynamic ensemble employed for averaging the initial conditions. The analysis yields explicit expressions for the Taylor coefficients which are then used to compute the errors. In the case of the algorithmically based practical numerical simulations in which fixed, albeit small, steps are repeatedly applied, the rise in the number of steps does not reduce the size of the steps but increases the total time of interest. The combinatorial formula shows that, here, the errors diverge. Furthermore, this work can be used to supplement other efforts such as the use of shadow Hamiltonians where the truncation of the series expansion of the latter will produce errors in the higher order propagator moments. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
30. Look before you leap: A confidence-based method for selecting species criticality while avoiding negative populations in τ-leaping.
- Author
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Yates, Christian A. and Burrage, Kevin
- Subjects
- *
CHEMICAL kinetics , *STOCHASTIC processes , *SIMULATION methods & models , *ALGORITHMS , *RANDOM variables , *APPROXIMATION theory , *DISTRIBUTION (Probability theory) , *NUMERICAL analysis - Abstract
The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes 'significantly' during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
31. Integral tau methods for stiff stochastic chemical systems.
- Author
-
Yang, Yushu, Rathinam, Muruhan, and Shen, Jinglai
- Subjects
- *
CHEMICAL systems , *STOCHASTIC systems , *NUMERICAL analysis , *COMPARATIVE studies , *APPROXIMATION theory , *SIMULATION methods & models , *NATURAL numbers - Abstract
Tau leaping methods enable efficient simulation of discrete stochastic chemical systems. Stiff stochastic systems are particularly challenging since implicit methods, which are good for stiffness, result in noninteger states. The occurrence of negative states is also a common problem in tau leaping. In this paper, we introduce the implicit Minkowski-Weyl tau (IMW-τ) methods. Two updating schemes of the IMW-τ methods are presented: implicit Minkowski-Weyl sequential (IMW-S) and implicit Minkowski-Weyl parallel (IMW-P). The main desirable feature of these methods is that they are designed for stiff stochastic systems with molecular copy numbers ranging from small to large and that they produce integer states without rounding. This is accomplished by the use of a split step where the first part is implicit and computes the mean update while the second part is explicit and generates a random update with the mean computed in the first part. We illustrate the IMW-S and IMW-P methods by some numerical examples, and compare them with existing tau methods. For most cases, the IMW-S and IMW-P methods perform favorably. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
32. Reconsidering an analytical gradient expression within a divide-and-conquer self-consistent field approach: Exact formula and its approximate treatment.
- Author
-
Kobayashi, Masato, Kunisada, Tomotaka, Akama, Tomoko, Sakura, Daisuke, and Nakai, Hiromi
- Subjects
- *
SELF-consistent field theory , *APPROXIMATION theory , *DENSITY matrices , *PERTURBATION theory , *NUMERICAL analysis , *PHYSICS periodicals , *SCIENCE publishing - Abstract
An analytical energy gradient formula for the density-matrix-based linear-scaling divide-and-conquer (DC) self-consistent field (SCF) method was proposed in a previous paper by Yang and Lee (YL) [J. Chem. Phys. 103, 5674 (1995)]. Since the formula by YL does not correspond to the exact gradient of the DC-SCF energy, we derive the exact formula by direct differentiation, which requires solving the coupled-perturbed equations while including the inter-subsystem coupling terms. Next, we present an alternative formula for approximately evaluating the DC-SCF energy gradient, assuming the variational condition for the subsystem density matrices. Numerical assessments confirmed that the DC-SCF energy gradient values obtained by the present formula are in reasonable agreement with the conventional SCF values when adopting a reliable buffer region. Furthermore, the performance of the present method was found to be better than that of the YL method. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
33. Interpolation of diabatic potential-energy surfaces: Quantum dynamics on ab initio surfaces.
- Author
-
Evenhuis, Christian R., Xin Lin, Dong H. Zhang, Yarkony, David, and Collins, Michael A.
- Subjects
- *
INTERPOLATION , *APPROXIMATION theory , *NUMERICAL analysis , *POTENTIAL energy surfaces , *QUANTUM chemistry , *QUANTUM theory - Abstract
A method for constructing diabatic potential-energy matrices from ab initio quantum chemistry data is described and tested for use in exact quantum reactive scattering. The method is a refinement of that presented in a previous paper, in that it accounts for the presence of the nonremovable derivative coupling. The accuracy of quantum dynamics on this type of diabatic potential is tested by comparison with an analytic model and for an ab initio description of the two lowest-energy states of H3. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
34. A q-polynomial approach to constacyclic codes.
- Author
-
Fang, Weijun, Wen, Jiejing, and Fu, Fang-Wei
- Subjects
- *
POLYNOMIALS , *APPROXIMATION theory , *NUMERICAL analysis , *NUMERICAL calculations - Abstract
As a generalization of cyclic codes, constacyclic codes is an important and interesting class of codes due to their nice algebraic structures and various applications in engineering. This paper is devoted to the study of the q -polynomial approach to constacyclic codes. Fundamental theory of this approach will be developed, and will be employed to construct some families of optimal and almost optimal codes in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
35. Stress intensity factor of radial cracks in isotropic functionally graded solid cylinders.
- Author
-
Mahbadi, H.
- Subjects
- *
CYLINDER (Shapes) , *SURFACE cracks , *STRESS intensity factors (Fracture mechanics) , *FUNCTIONALLY gradient materials , *APPROXIMATION theory , *NUMERICAL analysis - Abstract
This paper estimates stress intensity factors of rotating solid disks or cylinders with a radial crack subjected to a uniform tension at their outer surface and a uniform temperature change through the body. Material properties of the cylinder are assumed to obey from the power law through the radius of the cylinder. The cracks are assumed to be small and located radially at center, inside or edge of the body. The stress intensity factors are obtained applying an approximate method and using the proper geometric functions for combination of the thermomechanical stresses. The method proposed in this paper is imposed to isotropic FG plates with an edge slanted crack to quantify the difference between present method and numerical methods given in the literature review. Also, the SIFs obtained for the non-homogeneous cylinder are reduced to the homogeneous one and are compared with the corresponding exact solution of isotropic materials. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
36. A new look at the fractionalization of the logistic equation.
- Author
-
Ortigueira, Manuel and Bengochea, Gabriel
- Subjects
- *
LOGISTIC functions (Mathematics) , *FRACTIONAL calculus , *NUMERICAL analysis , *APPROXIMATION theory , *CAPUTO fractional derivatives - Abstract
The fractional version of the logistic equation will be studied in this paper. Motivated by unsuccessful previous papers, we showed how to obtain the correct solution. The algorithm is very simple. Its numerical implementation will be studied and exemplified using a Padé approximation. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
37. Do Orthogonal Polynomials Dream of Symmetric Curves?
- Author
-
Martínez-Finkelshtein, A. and Rakhmanov, E.
- Subjects
- *
ORTHOGONAL polynomials , *MATHEMATICAL symmetry , *RANDOM matrices , *NUMERICAL analysis , *APPROXIMATION theory - Abstract
The complex or non-Hermitian orthogonal polynomials with analytic weights are ubiquitous in several areas such as approximation theory, random matrix models, theoretical physics and in numerical analysis, to mention a few. Due to the freedom in the choice of the integration contour for such polynomials, the location of their zeros is a priori not clear. Nevertheless, numerical experiments, such as those presented in this paper, show that the zeros not simply cluster somewhere on the plane, but persistently choose to align on certain curves, and in a very regular fashion. The problem of the limit zero distribution for the non-Hermitian orthogonal polynomials is one of the central aspects of their theory. Several important results in this direction have been obtained, especially in the last 30 years, and describing them is one of the goals of the first parts of this paper. However, the general theory is far from being complete, and many natural questions remain unanswered or have only a partial explanation. Thus, the second motivation of this paper is to discuss some 'mysterious' configurations of zeros of polynomials, defined by an orthogonality condition with respect to a sum of exponential functions on the plane, that appeared as a results of our numerical experiments. In this apparently simple situation the zeros of these orthogonal polynomials may exhibit different behaviors: for some of them we state the rigorous results, while others are presented as conjectures (apparently, within a reach of modern techniques). Finally, there are cases for which it is not yet clear how to explain our numerical results, and where we cannot go beyond an empirical discussion. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
38. The conjugate gradient method for split variational inclusion and constrained convex minimization problems.
- Author
-
Che, Haitao and Li, Meixia
- Subjects
- *
CONJUGATE gradient methods , *APPROXIMATION theory , *SET theory , *MATHEMATICAL mappings , *NUMERICAL analysis , *FIXED point theory - Abstract
In this paper, we introduce and study a new viscosity approximation method based on the conjugate gradient method and an averaged mapping approach for finding a common element of the set of solutions of a constrained convex minimization problem and the set of solutions of a split variational inclusion problem. Under suitable conditions, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of the split variational inclusion problem and the set of solutions of the constrained convex minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area. Finally, preliminary numerical results indicate the feasibility and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
39. Solving Time Fractional Sharma-Tasso-Olever Equation by Optimal Homotopy Asymptotic Method.
- Author
-
Nawaz, Rashid and Zada, Laiq
- Subjects
- *
CAPUTO fractional derivatives , *HOMOTOPY theory , *APPROXIMATION theory , *NUMERICAL analysis , *PERTURBATION theory - Abstract
In this paper optimal homotopy asymptotic method (OHAM) with the help of Caputo derivative is used for time fractional Sharma-Tasso-Olever equation. Obtained results are compared with HPM and ADM. Numerical results shows that optimal homotopy asymptotic method gives more accurate solution than that of HPM and ADM even at 1st order approximation. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
40. High Order Approximation to New Generalized Caputo Fractional Derivatives and its Applications.
- Author
-
Xuhao Li and Wong, Patricia J. Y.
- Subjects
- *
GENERALIZABILITY theory , *APPROXIMATION theory , *DERIVATIVES (Mathematics) , *CAPUTO fractional derivatives , *NUMERICAL analysis - Abstract
In this paper, we shall develop a generalized L1 - 2 formula for new generalized fractional Caputo derivatives. It is theoretically shown that this new approximation achieves O(τ3-α ) (αis the step size) which improves earlier work done to date. Also, numerical tests and an application are presented to demonstrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
41. Numerical Approximation of Nonlinear Aeroelastic Problems by Stabilized Finite Element Method.
- Author
-
Sváček, Petr
- Subjects
- *
AEROELASTICITY , *APPROXIMATION theory , *NONLINEAR analysis , *FINITE element method , *NUMERICAL analysis - Abstract
The paper focuses on numerical solution of a nonlinear aeroelastic problem. The classical approach of linearized aerodynamic forces is compared to the numerical approximation of the coupled fluid-structure problem. In the second case the finite element method is used for solution of the incompressible Navier-Stokes equations and coupled with the non-linear motion equations of a flexibly supported airfoil. The obtained results are compared to the linearized approach approximations. The influence of the nonlinear terms is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
42. On Application of Acoustic Analogies with Numerical Aproximations of Fluid Flow with Low Mach Numbers.
- Author
-
Valášek, J. and Sváček, P.
- Subjects
- *
FLUID dynamics , *MACH number , *NUMERICAL analysis , *APPROXIMATION theory , *NAVIER-Stokes equations , *MATHEMATICAL models - Abstract
This paper focus on the numerical approximation of a fluid-structure-acoustic interaction problem. The two-dimensional non-linear fluid-structure interaction problem is mathematically modelled by the linear elastic problem coupled with the incompressible Navier-Stokes equations. The arbitrary Lagrangian-Eulerian method is used in order to treat the moving domain. The acoustic problem is solved with the perturbed convective wave equation analogy. The finite element discretization is described and the the modified streamline-upwind/Petrov-Galerkin stabilization is used for the flow problem. Numerical results are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
43. Explicit Saul'yev Finite Difference Approximation for Two-Dimensional Fractional Sub-diffusion Equation.
- Author
-
Ali, Umair and Abdullah, Farah Aini
- Subjects
- *
FINITE difference method , *NUMERICAL analysis , *APPROXIMATION theory , *DISCRETIZATION methods , *NUMERICAL solutions to differential equations - Abstract
In this paper, we discuss the development, analysis and implementation of the explicit Saul'yev difference scheme for the solution of two-dimensional time fractional sub-diffusion equations. The Grünwald-Letnikov formula is used for the discretization of the time fractional derivative of order α. The stability of the proposed scheme is analyzed. Finally, numerical examples are given to show the performance of the scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
44. KAOR Iterative Method with Cubic B-Spline Approximation for Solving Two-Point Boundary Value Problems.
- Author
-
Suardi, Mohd Norfadli, Mohd Radzuan, Nurul Zafira Farhana, and Sulaiman, Jumat
- Subjects
- *
ITERATIVE methods (Mathematics) , *NUMERICAL analysis , *ITERATIVE decoding , *APPROXIMATION theory , *BOUNDARY value problems - Abstract
The paper deals with the system of cubic B-spline approximation equation is generated by applying cubic Bspline discretization scheme in solving two-point boundary value problems (BVPs). Then, the system will be solved by using Kaudd Accelerated Over Relaxation (KAOR) iterative method. As comparison, the KAOR iterative method also consider with Gauss-Seidel (GS) and Successive Over Relaxation (SOR) on two numerical examples problem to observe the efficiency of these proposed methods are consider. From the numerical results have been recorded, it shows that the KAOR method is a superior method in term number of iteration and computational time. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
45. Bezier Curve Interpolation on Road Map by Uniform, Chordal and Centripetal Parameterization.
- Author
-
Saffie, Mohd Syakir and Ramli, Ahmad
- Subjects
- *
PARAMETERIZATION , *INTERPOLATION , *APPROXIMATION theory , *NUMERICAL analysis , *MATHEMATICAL functions - Abstract
This paper focuses on reconstructing the road curve by using Bezier curve fitting on a map with the aid of various parameterization approaches. A good fitting requires the Bezier curve fits closely to the road on a map without any major distortion that can be seen visually. Since the Bezier curve does not interpolate its control points, then designers had difficulties in determining the most ideal set of control points that can lead to a desired design. The parameterization method proposed by previous researchers may be very useful since the choice of control points had been automatically generated such that the curve will pass through the selected points on the road curve on a map. Differentparameterization techniques for fitting Bezier curve had been implemented in the perspective of road map fitting. One of the finding is that parameterization does not work well for a higher degree. By increasing control points, the curve is perturbed especially near both ends of the curve. The generated Bezier curve fitting may become worse if the actual road contains a lot of sharp corner. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
46. Fast Iterative Methods for Computing the Harmonic Information Potentials in Wireless Sensor Networks.
- Author
-
Saudi, Azali, Aris, Zakariah, and Awg Ismail, Zamhar Iswandono
- Subjects
- *
ITERATIVE methods (Mathematics) , *NUMERICAL analysis , *PARTIAL differential equations , *HARMONIC functions , *APPROXIMATION theory - Abstract
This paper presents a study on the dissemination of information from the source node by establishing information potentials that uses the information gradient descent method. The information gradient is computed by solving the discrete approximation of a partial difference equation. The solution to this equation is the harmonic functions which are also known as harmonic information potentials. Commonly used iterative method for solving partial difference equation to obtain the harmonic information potentials was the classical Jacobi that was found to be too slow when it dealt with large domain. This study proposes faster iterative methods using Gauss-Seidel and Successive Overrelaxation with Red-Black ordering strategy (GS-RB and SOR-RB), as well as Modified Successive Overrelaxation (MSOR) schemes. The experimental results show that the execution time of GS-RB, SOR-RB and MSOR are faster than the existing methods. The advantage of the proposed methods in terms of computational speed is clearly shown with increasingly large domain size. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
47. NUMERICAL ANALYSIS OF THE BEHAVIOUR OF A FLEXIBLE PILE FOUNDATION VERSUS A RIGID ONE UNDER LATERAL CYCLIC ACTION.
- Author
-
Loretta, BATALI, Andrei, DRĂGUŞIN, and Horaţiu, POPA
- Subjects
- *
PILES & pile driving , *STRUCTURAL geology , *TECTONIC landforms , *NUMERICAL analysis , *APPROXIMATION theory - Abstract
The purpose of the present paper is to analyse the behaviour of a flexible pile foundation versus a rigid one when submitted to lateral cyclic action coming from waves or wind, through numerical modelling using 3D finite elements. The comparison elements are: the maximum pile head displacement and the evolution of the maximum bending moment. The numerical modelling has been performed using the software CESAR-LCPC [1]. The study has been performed for 15 cycles, but the numerical model has also served to create some extrapolation functions allowing the analysis of a high number of cycles - up to 100000. The numerical model has been initially calibrated using the results of some small-scale centrifuge experimental tests performed by Frederic Rosquoët [2], officially obtained from IFSTTAR, Nantes [3]. The experimental results used for calibrating the numerical model were performed for a flexible pile. After that, on the calibrated model, the flexible pile has been changed into a rigid one and a comparison between them regarding the behaviour under lateral cyclic action has been performed. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
48. Numerical methods and analysis for a multi-term time–space variable-order fractional advection–diffusion equations and applications.
- Author
-
Chen, Ruige, Liu, Fawang, and Anh, Vo
- Subjects
- *
ADVECTION-diffusion equations , *FRACTIONAL calculus , *POROUS materials , *NUMERICAL analysis , *APPROXIMATION theory - Abstract
Abstract Field experiments of solute transport through heterogeneous porous and fractured media show that the growth of contaminant plumes may convert between diffusive states. In this paper, we propose a multi-term time–space variable-order fractional advection–diffusion model (MTT-SVO-FADM) to describe the underlying transport dynamics. We consider a numerical approach based on the implicit numerical method for numerical solution of this model. A fully-discrete numerical scheme is developed by using the classical finite difference method. The unconditional stability and convergence of the scheme are discussed and theoretically proved. We use a modified grid approximation method (MGAM) to estimate the model's parameters. The MTT-SVO-FADM is then applied to describe transient dispersion observed at a field tracer test and four numerical experiments. The results show that this model can simulate the experimental data more accurately and can efficiently quantify these transitions. Highlights • A multi-term time–space variable-order fractional advection–diffusion model is proposed. • A fully-discrete numerical scheme is developed. • The unconditional stability and convergence of the scheme are discussed and proved. • A modified grid approximation method is used to estimate the model's parameters. • This model is applied to describe transient dispersion observed at a field tracer test and four numerical experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
49. Numerical efficiency of some exponential methods for an advection-diffusion equation.
- Author
-
Macías-Díaz, Jorge Eduardo and İnan, Bilge
- Subjects
- *
ADVECTION-diffusion equations , *NUMERICAL analysis , *STOCHASTIC convergence , *APPROXIMATION theory , *BURGERS' equation - Abstract
In this paper, we investigate several modified exponential finite-difference methods to approximate the solution of the one-dimensional viscous Burgers' equation. Burgers' equation admits solutions that are positive and bounded under appropriate conditions. Motivated by these facts, we propose nonsingular exponential methods that are capable of preserving some structural properties of the solutions of Burgers' equation. The fact that some of the techniques preserve structural properties of the solutions is thoroughly established in this work. Rigorous analyses of consistency, stability and numerical convergence of these schemes are presented for the first time in the literature, together with estimates of the numerical solutions. The methods are computationally improved for efficiency using the Padé approximation technique. As a result, the computational cost is substantially reduced in this way. Comparisons of the numerical approximations against the exact solutions of some initial-boundary-value problems for different Reynolds numbers show a good agreement between them. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
50. Hierarchical Rasterization of Curved Primitives for Vector Graphics Rendering on the GPU.
- Author
-
Dokter, Mark, Hladky, Jozef, Parger, Mathias, Schmalstieg, Dieter, Seidel, Hans‐Peter, and Steinberger, Markus
- Subjects
- *
VECTOR graphics , *GRAPHICS processing units , *POLYGONS , *APPROXIMATION theory , *NUMERICAL analysis - Abstract
In this paper, we introduce the CPatch, a curved primitive that can be used to construct arbitrary vector graphics. A CPatch is a generalization of a 2D polygon: Any number of curves up to a cubic degree bound a primitive. We show that a CPatch can be rasterized efficiently in a hierarchical manner on the GPU, locally discarding irrelevant portions of the curves. Our rasterizer is fast and scalable, works on all patches in parallel, and does not require any approximations. We show a parallel implementation of our rasterizer, which naturally supports all kinds of color spaces, blending and super‐sampling. Additionally, we show how vector graphics input can efficiently be converted to a CPatch representation, solving challenges like patch self intersections and false inside‐outside classification. Results indicate that our approach is faster than the state‐of‐the‐art, more flexible and could potentially be implemented in hardware. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
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