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Carl David Tolmé Runge was a German mathematician. In 1895 he brought about a revolution in the science of what has become numerical analysis. Numerical approximation to the solution of ordinary differential equations had been based on the method of Euler. but it suffered from a low convergence rate. Runge's discovery in his 1895 paper brought the so-called order from 1 up to 2. This development was followed within a few years by extensions of his techniques which brought the possible order up to 4. The analysis of order conditions for early work on Runge-Kutta methods was based on the use of a scalar test problem y' = f (x, y), but for high order method derivations and other applications, it is appropriate to use instead an autonomous high dimensional test problem y' = f (y). Because of the special requirements of stiff problems, implicit Runge-Kutta methods have an importance of their own and these developments are briefly surveyed. The intricate manipulations required to analyse the order of complicated methods has lead to an algebraic theory and its formulation as B-series. Finally, the special applications to structure-preserving algorithms are introduced. [ABSTRACT FROM AUTHOR]

A disk Bézier curve is a Bézier curve whose control points are disks. It can be considered as a parametric curve with error tolerances. In this paper, we propose method to find G2-multi degree reduction of disk Bézier curves based on two stages. The center and the radius curves are degree reduced using G2-continuity in the first stage and minimizing the error of approximating the radius curve in the second stage. We give some examples and figures to demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the possible use of control theory, particularly theory on optimal control to derive some numerical methods for unconstrained optimization problems. Based upon this control theory, we derive a Levenberg-Marquardt-like method that guarantees greatest descent in a particular search region. The implementation of this method in its original form requires inversion of a non-sparse matrix or equivalently solving a linear system in every iteration. Thus, an approximation of the proposed method via quasi-Newton update is constructed. Numerical results indicate that the new method is more effective and practical. [ABSTRACT FROM AUTHOR]

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]

The solution of a singularly perturbed problem corresponds to a function with large gradients. Therefore the question of interpolation and numerical differentiation of such functions is relevant. The interpolation based on Lagrange polynomials on uniform mesh is widely applied. However, it is known that the use of such interpolation for the function with large gradients leads to estimates that are not uniform with respect to the perturbation parameter and therefore leads to errors of order O(1). To obtain the estimates that are uniform with respect to the perturbation parameter, we can use the polynomial interpolation on a fitted mesh like the piecewise-uniform Shishkin mesh or we can construct on uniform mesh the interpolation formula that is exact on the boundary layer components. In this paper the numerical differentiation formulas for functions with large gradients based on the interpolation formulas on the uniform mesh, which were proposed by A.I. Zadorin, are investigated. The formulas for the first and the second derivatives of the function with two or three interpolation nodes are considered. Error estimates that are uniform with respect to the perturbation parameter are obtained in the particular cases. The numerical results validating the theoretical estimates are discussed. [ABSTRACT FROM AUTHOR]

The solution of systems of linear algebraic equations (SLAEs) is very often the most time-consuming part of the computational process during the treatment of the original problems, because these systems can be very large (containing up to many millions of equations). It is, therefore, important to select fast, robust and reliable methods for the solution of SLAEs when large applications are to be run, also in the case where fast modern computers are available. Since the coefficient matrices of the systems are normally sparse (i.e., most of their elements are zeros), the first requirement is to exploit efficiently the sparsity. However, this is normally not sufficient when the systems are very large. The computation of preconditioners based on approximate LU-factorizations and their use in the efforts to increase further the efficiency of the calculations will be discussed in this paper. Computational experiments based on comprehensive comparisons of many numerical results that are obtained by using ten well-known methods for solving SLAEs (the direct Gaussian elimination and nine iterative methods) when the coefficient matrices are chosen from the "Sparse Matrix Market" are reported in this paper. Most of the methods are preconditioned Krylov sub-space algorithms. [ABSTRACT FROM AUTHOR]

In the ring of quaternionic polynomials there is no easy solution to the problem of finding a suitable definition of multiplicity of a zero. In this paper we discuss different notions of multiple zeros available in the literature and add a computational point of view to this problem, by taking into account the behavior of the well known Newton's method in the presence of such roots. [ABSTRACT FROM AUTHOR]

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]

In this paper we aim to construct reliable numerical schemes for the approximation of solutions to fractional boundary value problems. We focus on equations of the form D*αy(t) = f(t,y(t)), y(a) = y1, where D*α denotes the fractional derivative of Caputo type, the order α satisfies 0 < α < 1 and f is a suitably behaved function. We seek solutions over a finite interval [0,T] and 0 < a < T. We investigate the structural stability of the underlying problem and discuss the numerical stability of the numerical methods we construct. [ABSTRACT FROM AUTHOR]

This paper presents a modified Thiele-Werner algorithm to construct a kind of reliable vector-valued rational interpolants (RVRIs) and then studies their existence. The reliability of this method means that if a solution of the basic vector-valued rational interpolation problem exists, the method given in this paper finds it. Then a method for testing the existence for RVRIs and some methods for dealing with unattainable points for RVRIs are given. [ABSTRACT FROM AUTHOR]

Matching pursuit is an iterative method whereby a signal is decomposed into a linear combination of functions that are selected from a redundant dictionary. In the original paper by Mallat and Zhang, a dictionary of Gabor functions is proposed. Each Gabor function is the product of a Gaussian function with a complex sinusoid, and is specified by time, frequency and scale. Since these functions are qualitatively and quantitatively very similar to ultrasonic echoes, it is appropriate to use the matching pursuit method to decompose ultrasonic signals to locate and identify discrete echoes embedded in complex signals. In this paper, a modified implementation of the matching pursuit algorithm is described, where the algorithm is specifically designed for an efficient decomposition of ultrasonic signals. The size of the wavelet dictionary is adaptively determined by the spectrum of the ultrasonic signal and is further controlled by additional physically meaningful restrictions. In each iterative step, the pursuit of the matching function begins with a coarse grid in the parameter space of the dictionary, and the highest energy matching function is found by interpolation of this coarse grid over the parameters. The algorithm is applied to a variety of measured ultrasonic signals. Signals consisting of multiple echoes are successfully decomposed, and the individual wavelets are well-matched to the original echoes. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this paper, weighted G0- and G1-multi-degree reduction of Bézier curves are considered. The degree reduction of a given Bézier curve of degree n is used to write it as a Bézier curve of degree m;m < n. Exact degree reduction is not possible, and, therefore approximation methods are used. The weight function w[t] = 2t(1-t), t ϵ [0;1] is used with the L2 -norm in multi degree reduction with G0- and G1-continuity at the end points of the curve. Numerical results and comparisons show that the new methods suggests smaller approximation errors in the interior of the domain and proves to be competative in applications. [ABSTRACT FROM AUTHOR]

In this paper, we make a modification to the standard conjugate gradient method so that its search direction satisfies the sufficient descent condition. We prove that the modified conjugate gradient method is globally convergent under Armijo line search. Numerical results show that the proposed conjugate gradient method is efficient compared to some of its standard counterparts for large-scale unconstrained optimization. [ABSTRACT FROM AUTHOR]

In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

In this paper we present a two-dimensional extension of the staggered Lax-Friedrichs scheme for the approximate solution of hyperbolic conservation laws on unstructured grids. By evolving the numerical solution on two staggered grids, the proposed scheme avoids the resolution of the Riemann problems arising at the cell interfaces. The control cells of the original grid are regular triangular cells of a finite element triangulation, while the staggered dual cells are quadrilaterals constructed on the triangular cells of the original grid. The accuracy and stability of the scheme are investigated and classical problems arising in gas dynamics are solved. The obtained results are in good agreement with corresponding ones appearing in the literature thus confirming the efficiency and potential of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a triangular plane stress element is implemented based on the large increment method (LIM) to solve 2D continuum mechanics problems. In the LIM, after the governing equations are established using the generalized elemental force variables as primary unknowns, an iteration procedure is employed to obtain an optimised approximate solution of the problem. Two numerical examples are investigated to study the mesh convergence of the proposed triangular LIM element. Structured meshes as well as unstructured meshes with different element densities are generated to illustrate the convergence of the total strain energy in both examples. The numerical results obtained from the LIM (including the total strain energy, the displacement and the stress) are compared with the analytical solutions as well as the results from the commercial FEM software ABAQUS. All the results show that the performance of the LIM is as good as the FEM in linear elastic problems. A simple elastoplastic example suggests that the LIM may obtain better result than the FEM. [ABSTRACT FROM AUTHOR]

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]

Short time series prediction technique based on Bernstein polynomials is presented in this paper. Firstly, the straightforward Bernstein polynomial extrapolation scheme is improved by extending the interval of approximation. Secondly, the forecasting scheme is designed in the evolutionary computational setup which is based on the conciliation between the coarseness of the algebraic prediction and the smoothness of the time average prediction. Computational experiments with the test time series suggest that this time series prediction technique could be applicable for various forecasting applications. [ABSTRACT FROM AUTHOR]

We study numerically a free-boundary value problem for a non-classical heat equation. The paper considers the so-called boundary immobilization method. The case of a region that initially has zero thickness is considered. We compare three difference scheme approximations: semi-implicit, Crank- Nicolson and Keller-box scheme. Numerical experiments are also discussed. [ABSTRACT FROM AUTHOR]

The spectrum of the Laplace-Beltrami operator is a useful tool for various shape analysis problems as it provides an intrinsic, Fourier-like characterization of 3D shapes. The numerical computation of the Laplace-Beltrami spectrum is typically based on a triangular mesh representation of the 3D surface, which makes its robustness dependent upon the quality of triangulation. In this paper, we propose an alternative approach by approximating the Laplace-Beltrami spectrum with the Laplacian spectrum of a narrow band composed of regular cubes with the Neumann boundary condition, thus mesh quality is not an issue in our method. We validate our method by computing the spectrum of real anatomical shapes and comparing with the mesh-based method. [ABSTRACT FROM AUTHOR]

The approximation error approach has been earlier proposed to handle modelling, numerical and computational errors in inverse problems. The idea of the approach is to include the errors to the forward model and compute the approximate statistics of the errors using Monte Carlo sampling. This can be a computationally tedious task but the key property of the approach is that the approximate statistics can be calculated off-line before measurement process takes place. In nonstationary problems, however, information is accumulated over time, and the initial uncertainties may turn out to have been exaggerated. In this paper, we propose an importance weighing algorithm with which the approximation error statistics can be updated during the accumulation of measurement information. As a computational example, we study an estimation problem that is related to a convection-diffusion problem in which the velocity field is not accurately specified. [ABSTRACT FROM AUTHOR]

In this paper we find a new asymptotic expansion valid in enzymatic reactions where the total amount of enzyme exceeds greatly the total amount of substrate. In such case it is well known that the Michelis-Menten approximation is no longer valid; therefore our asymptotic expansion is a new tool to approximate in a closed form the concentrations of the reactants in presence of an enzyme excess. [ABSTRACT FROM AUTHOR]

An alternative to currently used two-phase flow equations is considered to resolve discontinuous solutions in gas-solid mixtures. The equations in the present paper are based on the theory of thermodynamically compatible systems of hyperbolic conservation laws. The conservative hyperbolic governing equations were solved using Godunov methods of centred-type. This solution is then employed in the source terms problem with Strang splitting technique to solve the general initial-value problem for the two-phase flow equations. Results are presented, demonstrating the accuracy of the numerical methods associated with of the proposed two-phase conservation laws. [ABSTRACT FROM AUTHOR]

In this paper the problem of the numerical approximation of a incompressible viscous fluid flow interacting with a flexible structure is considered. The problem is modelled with the aid of Reynolds equations together with k-ω turbulence model and structure motion is described by a system of ordinary differential equations. The problem is discretized in space by the Galerkin Least Squares stabilized FE method and the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian method. [ABSTRACT FROM AUTHOR]

In this paper, we describe a variant of a solution for a common problem in applied statistics—we offer a variant method for estimating the parameters of a dynamic system, and observe its magnitudes, which statistically depend on the sequence of states of the system that are not observed. The method is realized by means of the multipolynomial approximations algorithm (the MPA algorithm). The method is validated by applying it to a problem of correction of finite sets of nominal experimental data on which nominal functions are constructed equationsby means of interpolation from the current states of the system. Nominal experimental data are presented on a finite set of points covering the domains of definition of the nominal functions. The nominal equations of motion of the dynamical system are defined by the nominal functions. In this paper, the concrete example of the nominal equations of motion correspond to the longitudinal motion of the aircraft similar of the F-l6 aircraft. The nominal functions are the calculated aerodynamic characteristics. The nominal experimental data are recorded by means of experiments in a wind-tunnel. The outcomes of measurements of the parameters of motion of the aircraft act on inputs for the MPA algorithm on a segment of real flight. The MPA algorithm defines a 32×1-vector of estimates of parameters, which are additive corrections to the nominal experimental data. [ABSTRACT FROM AUTHOR]

Continuous constraint reasoning assumes the uncertainty of numerical variables within given bounds and propagates such knowledge through a network of constraints, reducing the uncertainty. In some problems there is also information about the plausibility distribution of values within such bounds. However, the classical constraint framework cannot accommodate that information. This paper describes how the continuous constraint programming paradigm may be extended, in order to accommodate some probabilistic considerations, bridging the gap between the pure interval-based approach, that does not consider likelihoods, and the pure stochastic approach, that does not guarantee the safety of the obtained results. [ABSTRACT FROM AUTHOR]

Meshless analysis based on the radial point interpolation method (RPIM) is effective for solving partial differential equations without a mesh structure of the analysis target. An alternative method that yields fast computation, called the modified radial point interpolation method (MRPIM), has been proposed for meshless analysis. Both methods are based on the idea that basis functions of the solution, called shape functions, are represented using radial basis functions (RBFs). The main difference between them is in the definition of the shape functions. In particular, MRPIM defines the shape functions at each small subdomain generated as a uniform division of the target domain, whereas RPIM does not require such divisions. This division does not work effectively for analysis with non-uniformly distributed nodes, since the subdomain construction process is independent of the node density. This paper presents a new RBF-based meshless method that is applicable to non-uniformly distributed nodes. [ABSTRACT FROM AUTHOR]

The determination of the number (n) of unobserved sources is an important issue in Blind Source Separation (BSS) of linear and instantaneous mixtures. However BSS is already a difficult task, so we generally assume that this number (n) is known and a priori fixed. In this paper, we address this issue as a Bayesian model selection problem and view the determination of this number (n) as a hypothesis testing problem via comparison of Bayes factors and study the computation of these factors by two numerical approximations: importance sampling from the posterior and simulated annealing sampling. Seeking for a general solution may be tricky to this problem, so we will be interested in blind separation of sparse sources modeled by a double exponential prior “π(.) ∝ exp(-λ|.|)”. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Systems of work are complex structures with specific characteristics, which require the use of probabilistic methods based on the use of instruments, both in the design phase and the stage of analysis and evaluation to ensure the safe conditions of work within them. This paper presents a methodological approach to probabilistic and statistical analysis and assessment of risk scenarios identified in the systems work. Statistical approach is based on quantification of what is rational and can be seen, this constitutes the probabilistic extrapolation to what can be reasonably inferred from these statistics to assess the probability of occurrence of less common events that can not be observed directly. [ABSTRACT FROM AUTHOR]

Study of coupled reaction diffusion systems are very useful in various branches of science and engineering. In this paper, we provide a methodology to construct the solution for the coupled reaction diffusion systems, with initial and boundary conditions, where the forcing function is the sum of an increasing and decreasing function. It is known that the generalized monotone method coupled with coupled lower and upper solutions yield monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. In addition, the interval of existence is guaranteed by the lower and upper solutions, which are relatively easy to compute. Using the lower and upper solutions as the initial approximation, we develop a method to compute the sequence of coupled lower and upper solutions on the interval or on the desired interval of existence. Further, if the uniqueness conditions are satisfied, the coupled minimal and maximal solutions converge to the unique solution of the reaction diffusion systems. We will provide some numerical results as an application of our numerical methodology. [ABSTRACT FROM AUTHOR]

This paper describes a numerical scheme which approximates the solution of a nonlinear mixed type functional differential equation from nerve conduction theory. The solution of such equation is defined in all the entire real axis and tends to known values at ±∞. A numerical method extended from linear case is developed and applied to solve a nonlinear equation. [ABSTRACT FROM AUTHOR]

We propose sixth-order approximations for semilinear parabolic systems that are based on fourth-order compact difference schemes combined with Richardson extrapolation. Within this paper, Richardson extrapolation is applied directly to the solution procedures used within existing numerical algorithms for realization of compact fourth-order difference schemes. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed finite difference discretization strategy. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. Unlike many other methods described in the literature the family of algorithms we propose has the property of guaranteed convergence. [ABSTRACT FROM AUTHOR]

We consider here a natural spline interpolation based on reduced data and the so-called exponential parameterization (depending on parameter α ϵ [0;1]). In particular, the latter is studied in the context of the trajectory approximation in arbitrary euclidean space. The term reduced data refers to an ordered collection of interpolation points without provision of the corresponding knots. The numerical verification of the intrinsic asymptotics α(ϵ) in γ approximation by natural spline ĝN3 is conducted here for regular and sufficiently smooth curve γ sampled more-or-less uniformly. We select in this paper the substitutes for the missing knots according to the exponential parameterization. The outcomes of the numerical tests manifest sharp linear convergence orders α(ϵ) = 1, for all α ϵ [0;1). In addition, the latter results in unexpected left-hand side discontinuity at α = 1, since as shown again here a sharp quadratic order α(1) = 2 prevails. Remarkably, the case of α(1) = 2 (derived for reduced data) coincides with the well-known asymptotics established for a natural spline to fit non-reduced data determined by the sequence of interpolation points supplemented with the corresponding knots (see e.g. [1]). [ABSTRACT FROM AUTHOR]

This paper presents a new solid boundary treatment algorithm for smoothed particle hydrodynamics (SPH). Two types of virtual particles are used to model the solid boundary, and information of the virtual particles can be obtained using enhanced SPH approximations from fluid particles. Numerical examples demonstrate that SPH with this new solid boundary algorithm can lead to smooth and accurate pressure field, even for complex solid boundaries. [ABSTRACT FROM AUTHOR]

In this paper analysis for Greedy-Like methods are presented. These methods include Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP) and Iterative Hard Thresholding (IHT) algorithms. The proposed analysis is based on the Restricted-Isometry-Property (RIP), establishing a near-oracle performance guarantee for each of these techniques. The signal is assumed to be corrupted by an additive random white Gaussian noise; and to have a K-sparse representation with respect to a known dictionary D. The results for the three algorithms are of the same type but uses different constants and different requirements on the cardinality of the sparse representation. [ABSTRACT FROM AUTHOR]

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements' stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigations show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements' family. [ABSTRACT FROM AUTHOR]

In this paper, an investigation of the pygmy dipole resonance (PDR) in 154Sm nucleus has been performed using quasi particle random-phase approximation (QRPA). Analysis of the numerical results indicates that both ΔK=1 and ΔK=0 branches plays significant role in formation of PDR. [ABSTRACT FROM AUTHOR]

Several benchmark studies in eddy currents have been proposed by the WFNDEC. Also, there are many analytical exact and approximate solution of interest to quantitatively evaluate the capability of numerical codes to predict the magnitude of the induced currents effects. In this paper we present the results obtained using COMSOL for a representative set of cases of interest. We analyze the accuracy of the results, but also the elements we believe are relevant from the perspective of the NDE specialist (simplicity, computer requirements, things to take into account to get good results, problems faced when solving, failures, etc.) [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-point implicit block method for solving delay differential equations. For greater efficiency, the block method is implemented in variable stepsize technique. The most optimal stepsize is taken while achieving the desired accuracy. The implicit method is solved using predictor-corrector scheme where the corrector is iterated until convergence. Grid point formulae are derived using a predictor and a corrector of order five. The formulae produce two new values in a single integration step. Delay solutions are approximated using Hermite interpolation of order five. The advantage of using Hermite interpolation is that it requires less support points than the existing interpolation technique in order to achieve the overall accuracy. Numerical results indicate that the two-point block method with Hermite interpolation technique is efficient and reliable in solving a wide range of delay differential equations. [ABSTRACT FROM AUTHOR]

This paper considers the implementation of fourth order direct method in the form of Adams Moulton method for solving directly second order delay differential equations. The proposed method approximates the solutions using constant step size. Numerical results are presented to show that the proposed code is suitable for solving second order delay differential equations. [ABSTRACT FROM AUTHOR]

Numerical methods of successive approximations can find the solution of single nonlinear equations. These includes numerical-iterative and hybrids methods such as Newton's method, Secant method, Muller's method, x = g(x) method and Regula Falsi method. One of the recent studies is the higher order homotopy Taylor-perturbation methods via start-system (HHTPss) that have shown promising results. Theoretical considerations such as stability, consistency and convergence have yet being given much attention. Thus, this paper considers the theoretical aspects of the HHTPss numerical schemes used to solve the nonlinear equations. Theoretical and numerical results obtained relating to the stability, consistency and convergence of the schemes are verified by data from computational experiments, Maple14. [ABSTRACT FROM AUTHOR]

This paper focuses on recently proposed Enhanced Multivariance Product Representation (EMPR) for multivariate functions. This method has been proposed to approximate the multivariate functions by certain additive less variate functions via support functions to get better quality than HDMR's. For this purpose, EMPR disintegrates a multivariate function to components which are respectively constant, univariate, bivariate and so on in ascending multivariance. This work aims at the investigation of the EMPR truncation qualities with respect to the selection of the support functions. [ABSTRACT FROM AUTHOR]

In this paper we develop a second order, positive preserving explicit-implicit numerical method for solving Keller-Segel system of degenerate type. The approximation is based on finite volume method and flux-limiter technique in space and explicit Euler method in time. In order to save computational time we use decoupling procedure for solving the discrete system. Numerical results are also presented. [ABSTRACT FROM AUTHOR]

A mathematical model for haematopoietic stem cells migration towards their niche in the bone marrow has been proposed in the literature. It consists of a chemotaxis system of partial differential equations with nonlinear boundary conditions and an additional ordinary differential equation on a part of the computational boundary. The aim in the current paper is first to answer some of the open questions of a recently introduced finite volume scheme for this chemotaxis system of differential equations and second to investigate the influence of the boundary conditions on the choice of flux limiters (the generalized minmod, Koren, van Leer limiters are investigated) used to ensure positivity and non-oscillating nature of the numerical solution. [ABSTRACT FROM AUTHOR]