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This paper investigates the problem of robust stability of uncertain linear discrete-time system over network with bounded packet loss. A new Lyapunov functional is constructed. It can more fully utilize the characteristics of the packet loss; hence the established stability criterion is more effective to deal with the effect of packet loss on the stability. Numerical examples are given to illustrate the effectiveness and advantage of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which is C1 in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled. Some numerical examples are illustrated in the end of this paper. [ABSTRACT FROM AUTHOR]

In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stages. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R H and R P ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R P and R H ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection model R H P is less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is max 7 , 17 = 17. Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates β 1 and β 2 , respectively. The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R 0 , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R 0 > 1. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R 0 < 1 , and the unique endemic equilibrium point is locally asymptotically stable whenever R 0 > 1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R 0 = 1 , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R 0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis. [ABSTRACT FROM AUTHOR]

In this paper, the analyses of traffic evolution on the road network of a roundabout having three entrances and three exiting legs are conducted from macroscopic point of view. The road networks of roundabouts are modeled as a merging and diverging types 1 × 2 and 2 × 1 junctions. To study traffic evolution at junction, two cases have been considered, namely, demand and supply limited cases. In each case, detailed mathematical analysis and numerical tests have been presented. The analysis in the case of demand limited showed that rarefaction wave fills the portion of the road network in time. In the contrary, in supply limited case, traffic congestion occurs at merging junctions and shock wave propagating back results in reducing the performance of a roundabout to control traffic dynamics. Also, we illustrate density and flux profiles versus space discretization at different time steps via numerical simulation with the help of Godunov scheme. [ABSTRACT FROM AUTHOR]

This paper deals with an inverse problem for identifying an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. Since this problem is illposed, we obtain the regularization solution by the modified regularization method. Furthermore, we obtain the Hõlder-type error estimate between the regularization solution and the exact solution. The numerical results show that the proposed method is stable and the unknown source is recovered very well. [ABSTRACT FROM AUTHOR]

One important and valuable topic in rough sets is attribute reduction of a decision system. The existing attribute reductions are designed to just keep confidence of every certain rule as they cannot identify key conditional attributes explicitly for special decision rules. In this paper, we develop the concept of ?-local reduction in order to offer a minimal description for special ?- possible decision rules. The approach of discernibility matrix is employed to investigate the structure of a ?-local reduction and compute all ?-local reductions. An example of medical diagnosis is employed to illustrate our idea of the ?-local reduction. Finally, numerical experiments are performed to show that our method proposed in this paper is feasible and valid. [ABSTRACT FROM AUTHOR]

In previous laboratory study, we have shown the thermal behavior of Keke Ya light crude oil (Tarim oilfield, branch of CNPC) for high-pressure air injection (HPAI) application potential study. To clarify the influences of thermal effects on oil production, in this paper, we derived a mathematical model for calculating oil flow rate, which is based on the heat conduction property in porous media from the combustion tube experiment. Based on remarkably limited knowledge consisting of very global balance arguments and disregarding all the details of the mechanisms in the reaction zone, the local governing equations are formulated in a dimensionless form. We use finite difference method to solve this model and address the study by way of qualitative analysis. The time-space dimensionless oil flow rate (qD) profiles are established for comprehensive studies on the oil flow rate characteristic affected by thermal effects. It also discusses how these findings will impact HPAI project performances, and several guidelines are suggested. [ABSTRACT FROM AUTHOR]

This paper deals with the approximation of systems of differential-algebraic equations based on a certain error functional naturally associated with the system. In seeking to minimize the error, by using standard descent schemes, the procedure can never get stuck in local minima but will always and steadily decrease the error until getting to the solution sought. Starting with an initial approximation to the solution, we improve it by adding the solution of some associated linear problems, in such a way that the error is significantly decreased. Some numerical examples are presented to illustrate the main theoretical conclusions. We should mention that we have already explored, in some previous papers (Amat et al., in press, Amat and Pedregal, 2009, and Pedregal, 2010), this point of view for regular problems. However, the main hypotheses in these papers ask for some requirements that essentially rule out the application to singular problems. We are also preparing a much more ambitious perspective for the theoretical analysis of nonlinear DAEs based on this same approach. [ABSTRACT FROM AUTHOR]

We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the weight is variable. Obviously, this new method will generalize a number of applications of reproducing kernel theory to many areas. [ABSTRACT FROM AUTHOR]

This paper begins with presenting a mathematical model for contaminant transport in the fractured vuggy porous media of a species of contaminant (PCP). Two phases are numerically simulated for a process of contaminant and clean water infiltrated in the fractured vuggy porous media by coupling mixed finite element (MFE) method and finite volume method (FVM), both of which are locally conservative, to approximate the model. A hybrid mixed finite element (HMFE) method is applied to approximate the velocity field for the model. The convection and diffusion terms are approached by FVM and the standard MFE, respectively. The pressure distribution and temporary evolution of the concentration profiles are obtained for two phases. The average effluent concentration on the outflow boundary is obtained at different time and shows some different features from the matrix porous media. The temporal multiscale phenomena of the effluent concentration on the outlet are observed. The results show how the different distribution of the vugs and the fractures impacts on the contaminant transport and the effluent concentration on the outlet. This paper sheds light on certain features of karstic groundwater are obtained. [ABSTRACT FROM AUTHOR]

The aim of this present paper is to establish the Poincaré-Bertrand formula for the double-layer potential on piecewise Lyapunov curve of integration. [ABSTRACT FROM AUTHOR]

The solution of least squares support vector machines (LS-SVMs) is characterized by a specific linear system, that is, a saddle point system. Approaches for its numerical solutions such as conjugate methods Sykens and Vandewalle (1999) and null space methods Chu et al. (2005) have been proposed. To speed up the solution of LS-SVM, this paper employs the minimal residual (MINRES) method to solve the above saddle point system directly. Theoretical analysis indicates that the MINRES method is more efficient than the conjugate gradient method and the null space method for solving the saddle point system. Experiments on benchmark data sets show that compared with mainstream algorithms for LS-SVM, the proposed approach significantly reduces the training time and keeps comparable accuracy. To heel, the LS-SVM based on MINRES method is used to track a practical problem originated from blast furnace iron-making process: changing trend prediction of silicon content in hot metal. The MINRES method-based LS-SVM can effectively perform feature reduction and model selection simultaneously, so it is a practical tool for the silicon trend prediction task. [ABSTRACT FROM AUTHOR]

This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just On. Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods. [ABSTRACT FROM AUTHOR]

Nowadays, quantum systems have become one of the focuses of the ongoing research and they are typical complex systems, whose state variables are defined on the complex field. In this paper, the issue of reachability and observability is addressed for a class of linear impulsive systems on complex field, for simplicity, complex linear impulsive systems. This kind of time-driven impulsive systems allows free impulsive instants, which leads to the limitation of using traditional definitions of reachability and observability directly. New notations about the span reachable set and unobservable set are proposed. Sufficient and necessary conditions for span reachability and observability of such systems are established. Moreover, the explicit characterization of span reachable set and unobservable set is presented by geometric analysis. It is pointed out that the geometric conditions are equivalent to the algebraic ones in known results for special cases. Numerical examples are also presented to show the effectiveness of the proposedmethods. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the design of lock gates submitted to ship impacts. In this paper, a simplified analytical method is presented to evaluate the resistance of such structures under collision. The basic idea is to assume that the resistance is first provided through a local deforming mode, corresponding to a localized crushing of some impacted structural elements. For consecutive larger deformations, the resistance is then mostly provided through a global deforming mode, corresponding to an overall movement of the entire gate. For assessing the resistance in the case of the local deforming mode, the structure is divided into a given number of large structural entities called "superelements." For each of them, a relation between the resistance of the gate and the penetration of the striking ship is established. However, as some results are already available in the literature, this subject is not treated extensively in this paper. On the contrary, the calculation of the resistance of the gate provided through the global mode is detailed and the strategy to switch from local to global deformation is highlighted. Finally, we propose to validate our developments by making a comparison between results obtained numerically and those predicted by the present analytical approach. [ABSTRACT FROM AUTHOR]

The theory of approximate solution lacks development in the area of nonlinear q-difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two q-polynomials are not easily found. In this paper, the formula for the multiplication of two q-polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear q-difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear q-difference equations. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the convergence of the Euler method to stochastic differential equations with piecewise continuous arguments(SEPCAs). The classical Khasminskiitype theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations (SDEs) without the linear growth condition by the use of the Lyapunov functions. However, there is no such result for SEPCAs. Firstly, this paper shows SEPCAs which have nonexplosion global solutions under local Lipschitz condition without the linear growth condition. Then the convergence in probability of numerical solutions to SEPCAs under the same conditions is established. Finally, an example is provided to illustrate our theory. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of finite-time H∞ filtering for one family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Initially, the definitions of singular stochastic finite-time boundedness and singular stochastic H∞ finitetime boundedness are presented. Then, the H∞ filtering is designed for the class of singular stochastic systems with or without uncertain parameters to ensure singular stochastic finitetime boundedness of the filtering error system and satisfy a prescribed H∞ performance level in some given finite-time interval. Furthermore, sufficient criteria are presented for the solvability of the filtering problems by employing the linear matrix inequality technique. Finally, numerical examples are given to illustrate the validity of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which tends to the exact solution of the problem. Furthermore, variational iteration method does not require the discretization of the problem. Two numerical examples are presented to illustrate the strength of the method. [ABSTRACT FROM AUTHOR]

An algebraic multigrid AMG( with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation DPA( scheme firstly proposed by Y. Notay 2006( as the coarsening method. We compare it with the smoothed aggregation algebraic multigrid and meanwhile show shifted Laplacian preconditioners. According to numerical results, we find that DPA algorithm is a good choice in AMG for Helmholtz equations in reducing time and memory. Spectral estimation of system preconditioned by the three methods and the influence of second-order and fourth-order accurate discretizations on the three techniques are also considered. [ABSTRACT FROM AUTHOR]

This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential ?-method is applied to p(t)D ß0?µp(t-t)/(?µ)(pµ(t-t))-?p(t) and it is shown that the exponential ?-method has the same order of convergence as that of the classical ?-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustratedwith numerical examples. [ABSTRACT FROM AUTHOR]

Decisions in the real-world contexts are often made in the presence of multiple, conflicting, and incommensurate criteria. Multiobjective programming methods such as multiple objective linear programming (MOLP) are techniques used to solve such multiple-criteria decision-making (MCDM) problems. One of the first interactive procedures to solve MOLP is STEMmethod. In this paper we try to improve STEM method in a way that we search a point in reduced feasible region whose criterion vector is closest to positive ideal criterion vector and furthest to negative ideal criterion vector. Therefore the presented method tries to increase the rate of satisfactoriness of the obtained solution. Finally, a numerical example for illustration of the new method is given to clarify the main results developed in this paper. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to present a minmax programming model for the optimal dispatch of Traffic and Patrol Police Service Platforms with single traffic congestion. The objective is to minimize the longest time of the dispatch for Traffic and Patrol Police Service Platforms. Some numerical experiments are carried out, and the optimal project is given. [ABSTRACT FROM AUTHOR]

In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta (RK) methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase-fitted and amplification-fitted. The linear stability and phase properties of the new methods are examined. The results of numerical experiments on physical and biological problems show the robustness and competence of the new methods compared to some highly efficient integrators in the literature. [ABSTRACT FROM AUTHOR]

This paper focuses on solving systems of nonlinear equations numerically. We propose an efficient iterative scheme including two steps and fourth order of convergence. The proposed method does not require the evaluation of second or higher order Frechet derivatives per iteration to proceed and reach fourth order of convergence. Finally, numerical results illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

This paper studies the finite element (FE) approximation to a second-type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconforming EQrot FE schemes under a reasonable regularity of the exact solution u ∊ H5/2(O), which seem to be never discovered in the previous literature. The optimal L²-norm error estimate is also derived for EQrot FE. At last, some numerical results are provided to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper employs the numerical assembly method (NAM) to determine the exact frequencyresponse amplitudes of an offshore structure such as piles or towers having the form of a hollow column filled with multiple fluids, immersed in water, carrying an eccentric tip mass supported by a translational spring and/or a rotational spring, and subjected to a harmonic force. The hollow column is modeled as a Bernoulli-Euler cantilever beam fixed at the bottom. For the case of zero harmonic force, the simultaneous equations of the vibration system reduce to an eigenvalue problem so that the natural frequencies and mode shapes of the beam can also be obtained. The effect of height of filled fluids on the characteristics of free vibration is also presented. [ABSTRACT FROM AUTHOR]

Harmony search (HS) method is an emerging metaheuristic optimization algorithm. In this paper, an improved harmony search method based on differential mutation operator (IHSDE) is proposed to deal with the optimization problems. Since the population diversity plays an important role in the behavior of evolution algorithm, the aim of this paper is to calculate the expected population mean and variance of IHSDE from theoretical viewpoint. Numerical results, compared with the HSDE, NGHS, show that the IHSDE method has good convergence property over a test-suite of well-known benchmark functions. [ABSTRACT FROM AUTHOR]

The temporal discretization scheme is one important ingredient of efficient simulator for two-phase flow in the fractured porous media. The application of single-scale temporal scheme is restricted by the rapid changes of the pressure and saturation in the fractured system with capillarity. In this paper, we propose a multi-scale time splitting strategy to simulate multi-scale multi-physics processes of two-phase flow in fractured porous media. We use the multi-scale time schemes for both the pressure and saturation equations; that is, a large time-step size is employed for the matrix domain, along with a small time-step size being applied in the fractures. The total time interval is partitioned into four temporal levels: the first level is used for the pressure in the entire domain, the second level matching rapid changes of the pressure in the fractures, the third level treating the response gap between the pressure and the saturation, and the fourth level applied for the saturation in the fractures. This method can reduce the computational cost arisen from the implicit solution of the pressure equation. Numerical examples are provided to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The present paper is the first in a series of works devoted to the solvability of the Possio singular integral equation. This equation relates the pressure distribution over a typical section of a slender wing in subsonic compressible air flow to the normal velocity of the points of a wing (downwash). In spite of the importance of the Possio equation, the question of the existence of its solution has not been settled yet.We provide a rigorous reduction of the initial boundary value problem involving a partial differential equation for the velocity potential and highly nonstandard boundary conditions to a singular integral equation, the Possio equation. The question of its solvability will be addressed in our forthcoming work. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints. The goal of this problem is to design a control input numerically, which is the damping and distributes locally on a subinterval of the region occupied by the beam, such that the total energy of the beam and the control on a given time period is minimal. We firstly use the finite element method (FEM) to obtain a finite-dimensional model based on the original PDE system. Then, using the control parameterization method, we approximate the finite-dimensional problem by a standard optimal parameter selection problem, which is a suboptimal problem and can be solved numerically by nonlinear mathematical programming algorithm. At last, some simulation studies will be presented by the proposed numerical approximation method in this paper, where the damping controls act on different locations of the Euler-Bernoulli beam. [ABSTRACT FROM AUTHOR]

The aim of this paper is attempting to explore the optimal way of supply chain management within the domain of environmental responsibility and concerns. The background of this research involves the issue of green supply chain management (GSCM) and the concept of the multiobjective integrated logistics model. More specifically, in this paper, we suggest the fuzzy multiobjective integrated logistics model with the transportation cost and demand fuzziness to solve green supply chain problems in the uncertain environment which is illustrated via the detailed numerical example. Results and the sensitivity analysis of the numerical example indicate that when the governmental subsidy value increased the profits of the reverse chain also increased. The finding shows that the governmental subsidy policy could remain of significant influence for used-product reverse logistics chain [ABSTRACT FROM AUTHOR]

An intuitive model is proposed in this paper to describe the electrical behavior of certain ultracapacitors. The model is based on a simple expression that can be fully characterized by five real numbers. In this paper, the measured impedances of three ultracapacitors as a function of frequency are compared to model results. There is good agreement between the model and measurements. Results presented in a previous study are also reviewed and the paper demonstrates that those results are also consistent with the newly described model. [ABSTRACT FROM AUTHOR]

The location selection of a logistics center is a crucial decision relating to cost and benefit analysis in airline industry. However, it is difficult to be solved because there are many conflicting and multiple objectives in location problems. To solve the problem, this paper integrates fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) andmultichoice goal programming (MCGP) to obtain an appropriate logistics center from many alternative locations for airline industry. The proposed method in this paper will offer the decision makers (DMs) to set multiple aspiration levels for the decision criteria. A numerical example of application is also presented. [ABSTRACT FROM AUTHOR]

Given current fast-changing market conditions and difficulty in obtaining financing for small- and medium-sized enterprises, this paper studies the robust inventory financing model under partial information, that is, where the demand distribution is partly known. Two demand information cases are discussed: (1) the mean and variance and (2) the support of the demand distribution. In this setting, the robust method that maximizes the worst-case profit and minimizes the firm's maximum possible regret of not acting optimally would be used to formulate the optimal sales quantity. We show that the approach used in this paper is tractable, and we provide an explicit expression for the robust optimal policy. We then use numerical examples to compare the firm's losses under two demand information cases with those occurring under demand certainty. More importantly, the numerical examples indicate that our robust inventory financing model can obtain a robust but not conservative solution. [ABSTRACT FROM AUTHOR]

This paper discusses why the selection of a finite planning horizon is preferable to an infinite one for a replenishment policy of production inventorymodels. In a production inventory model, the production rate is dependent on both the demand rate and the inventory level. When there is an exponentially decreasing demand, the application of an infinite planning horizon model is not suitable. The emphasis of this paper is threefold. First, while pointing out questionable results from a previous study, we propose a corrected infinite planning horizon inventory model for the first replenishment cycle. Second, while investigating the optimal solution for the minimization problem, we found that the infinite planning horizon should not be applied when dealing with an exponentially decreasing demand. Third, we developed a new production inventory model under a finite planning horizon for practitioners. Numerical examples are provided to support our findings. [ABSTRACT FROM AUTHOR]

Feature selection is an essential process in data mining applications since it reduces amodel's complexity. However, feature selection with various types of costs is still a newresearch topic. In this paper, we study the cost-sensitive feature selection problem of numeric data with measurement errors. Themajor contributions of this paper are fourfold. First, a newdatamodel is built to address test costs andmisclassification costs as well as error boundaries. It is distinguished fromthe existing models mainly on the error boundaries. Second, a covering-based rough set model with normal distributionmeasurement errors is constructed. With this model, coverings are constructed from data rather than assigned by users. Third, a new cost-sensitive feature selection problem is defined on this model. It is more realistic than the existing feature selection problems. Fourth, both backtracking and heuristic algorithms are proposed to deal with the new problem. Experimental results show the efficiency of the pruning techniques for the backtracking algorithm and the effectiveness of the heuristic algorithm. This study is a step toward realistic applications of the cost-sensitive learning. [ABSTRACT FROM AUTHOR]

This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a highorder compact PRADI likemethod. Both of themhave the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical results are presented to show the accuracy and efficiency of the new algorithms. [ABSTRACT FROM AUTHOR]

The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (x, y) is divided into two types: interior point and exterior point. The value of Hermite interpolation polynomial on a triangle will be used as the approximate value if point (x, y) is an interior point, while the value of a Hermite interpolation function with the form of weighted combination will be used if it is an exterior point. Hermite interpolation needs the first-order derivatives of the interpolated function which is not directly given in scatted data, so this paper also gives the approximate derivative at every scatted point using local radial basis function interpolation. And numerical tests indicate that the proposed piecewise bivariate Hermite interpolations are economic and have good approximation capacity. [ABSTRACT FROM AUTHOR]

The problem considered in this paper is to approximate the simple zeros of the function f(x) by iterative processes. An optimal 16th order class is constructed. The class is built by considering any of the optimal three-step derivative-involved methods in the first three steps of a four-step cycle in which the first derivative of the function at the fourth step is estimated by a combination of already known values. Per iteration, each method of the class reaches the efficiency index 5 √16 ≈ 1.741, by carrying out four evaluations of the function and one evaluation of the first derivative. The error equation for one technique of the class is furnished analytically. Some methods of the class are tested by challenging the existing high-order methods. The interval Newton's method is given as a tool for extracting enough accurate initial approximations to start such high-order methods. The obtained numerical results show that the derived methods are accurate and efficient. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain more general forms than the papers of (Jun et al. (2010); Jun et al. (in press)). The notions of N-subalgebras of types (∊, qk), (∊,∊ ∨qk), and (q,∊ ∨qk) are introduced, and the concepts of qk-support and∊ ∨qk-support are also introduced. Several related properties are investigated. Characterizations of N-subalgebra of type (∊,∊ ∨qk) are discussed, and conditions for an N-subalgebra of type (∊,∊ ∨qk) to be an N-subalgebra of type (∊, ∊) are considered. [ABSTRACT FROM AUTHOR]

Based on the model of symmetric and asymmetric duopoly option game, this paper discusses the present value of profit flows and the sunk investment costs for the trapezoidal fuzzy number. It constructs the fuzzy expressions of the investment value and investment threshold of followers and leaders under fuzzy environment and conducts numerical analysis. This offers a kind of explanation to the investment strategies under fuzzy environment. [ABSTRACT FROM AUTHOR]

The numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler's method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. The main aim is to investigate the convergence of the Eulermethod in probability to such equations with non-Lipschitz coefficients. Numerical example is given to demonstrate our results. [ABSTRACT FROM AUTHOR]

Stochastic systems with Markovian switching have been used in a variety of application areas, including biology, epidemiology, mechanics, economics, and finance. In this paper, we study the Euler-Maruyama (EM) method for neutral stochastic functional differential equations with Markovian switching. The main aim is to show that the numerical solutions will converge to the true solutions. Moreover, we obtain the convergence order of the approximate solutions. [ABSTRACT FROM AUTHOR]

We establish a general existence result for Galerkin's approximate solutions of abstract semilinear equations and conduct an error analysis. Our results may be regarded as some extension of a precedent work (Schultz 1969). The derivation of our results is, however, different from the discussion in his paper and is essentially based on the convergence theorem of Newton's method and some techniques for deriving it. Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations. [ABSTRACT FROM AUTHOR]

A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable. [ABSTRACT FROM AUTHOR]

The problems of mean-square exponential stability and robust H∞ control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities (LMIs). Then, H∞ performance is studied and robust H∞ controller is designed. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria. [ABSTRACT FROM AUTHOR]