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This paper presents a finite difference method for the Rosenau-Kawahara equation, which is performed under pseudo-compactness; this facilitates accuracy improvement. It is shown that the proposed s...

In this paper we present an application of the Generalized Finite Difference Method to solve the generalized nonlinear Benjamin–Bona–Mahony–Burgers equation in 2D and 3D. We provide two approaches ...

In this paper, we consider stochastic differential equations with locally Lipschitz coefficients. Two classes of balanced Euler method are presented. Their moment boundedness and their convergence ...

The current paper proposes a new high-order finite difference scheme with low computational complexity to solve the space-time fractional tempered diffusion equation. At the first stage, the time d...

A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix ...

In this paper, we consider Galerkin and multi-Galerkin methods and their iterated versions for solving the nonlinear Hammerstein-type integral equation on the half-line with sufficiently smooth ker...

In this paper, an efficient finite difference scheme is proposed for one dimension and two dimension coupled space fractional nonlinear Schrodinger equations. First, the high-order difference schem...

In this article we present the compensated two-step Maruyama methods for the stochastic differential equations with Poisson jumps. Mean-square (M-S) order convergence 12 is established and M-S stab...

In this paper, we investigate a numerical scheme for the singular Emden–Fowler problem using quintic B-spline. We eliminate the singularity of the problem according to Lopita's law and obtain a new...

In this paper, we propose a second-order implicit–explicit (IMEX) time-stepping scheme for the Gray-Scott (GS) model. In order to achieve a fast, stable and efficient scheme in time, we develop a l...

Reproducing kernel theories have attracted much attention for solving various problems. However, discussions of stability and convergence order are very difficult in the traditional reproducing ker...

A nonlinear initial boundary value problem with a time Caputo derivative of fractional-order β∈(1,2) and a space Riesz derivative of fractional-order α∈(1,2) is considered. A linearized alternating...

In the paper, the space second-order conservative characteristic finite difference method for solving convection–diffusion equations is developed and analysed. Applying the directional derivative a...

We propose and analyse a nonconforming finite element method for numerical approximation of the solution of a parabolic variational inequality associated with general obstacle. In this article, we ...

In this paper, we investigate how many convergence orders of discontinuous Galerkin (DG) method for numerically solving neutral delay differential equations (NDDEs). Although discontinuous behaviou...

In this paper, a finite difference-based numerical approach is developed for time-fractional Schrodinger equations with one or multidimensional space variables, with the use of fractional linear mu...

In this paper, a high-accuracy conservative difference scheme is presented for solving the space fractional Zakharov system, which preserves the original conservative properties. By virtue of the s...

This paper develops and analyses a finite difference/spectral-Galerkin scheme for the nonlinear fractional Schrodinger equations with Riesz space- and Caputo time-fractional derivatives. The L 1 fi...

The content of this paper is twofold. First, it aims to provide some new Newton-like methods for solving the root-finding problem in the complex plane. Moreover a convergence test for the resulted ...

A higher-order uncoupled finite difference scheme is proposed and analysed to approximate the solutions of the symmetric regularized long-wave equation. The finite difference technique preserving t...

In this paper, the numerical method for semi-linear stochastic variable delay integro-differential equations is studied. The stability of analytic solutions of semi-linear stochastic variable delay...

Fractal approximation is a well studied concept, but the convergence of all the existing fractal approximants towards the original function follows usually if the magnitude of the corresponding sca...

Waveform relaxation method at the PDE level can simplify the original differential system by several decoupling approaches, which is very useful for the iterative solution of nonlinear differential...

SIMSEK, Necip/0000-0003-3061-5770; Erturk, Muzeyyen/0000-0002-5328-7995 WOS: 000532204500001 In this paper we propose an S-iterative algorithm for finding the common element of the set of solutions of the variational inequalities and the set of fixed points of nonexpansive mappings. We study the convergence criteria of the mentioned algorithm under some mild conditions. As an application, a modified algorithm is suggested to solve convex minimization problems. Numerical examples are given to validate the theoretical findings obtained herein. Our results may be considered as an improvement, refinement and complement of the previously known results.

The modified anomalous sub-diffusion equation (MASDE) describes processes that become less anomalous as time progresses. In this paper, based on Crank-Nicolson and weighted and shifted Grunwald dif...

In this paper, we propose two inertial algorithms with new stepsize rule for solving a monotone and Lipschitz variational inequality in a Hilbert space and prove some weak and strong convergence th...

The aim of this paper is to study the convergence rates of the finite difference methods (FDMs) for solving the PDEs with spatial delays which arise in the option pricing under regime switching har...

We provide a concise overview of some iterative approaches, by which large and sparse eigenvalue problems are successfully dealt with. Our main goal in this paper is to prove the global convergence...

An adaptive continuous interior multi-penalty finite element method (ACMPFEM) for symmetric second-order linear elliptic equations is considered. The proposed ACMPFEM is defined using a bilinear fo...

In this note a sufficient condition for the convergence of the irrational Halley’s formula for solving nonlinear equations is obtained. In addition, we propose a new proof for the third-order conve...

In this paper, some accelerated iterative algorithms are developed to find the minimal positive solution of the nonsymmetric algebraic Riccati equation arising in transport theory. The convergence ...

In this paper, we discuss the USSOR method for solving indefinite least squares problem. The convergence conditions and algorithm of the USSOR method for solving indefinite least squares problem ar...

This article is devoted to the study of high-order conservative linearized finite difference scheme for a model of nonlinear dispersive equation: regularized long-wave-Korteweg–de Vries equation. I...

We consider the numerical approximation for a time fractional Schrodinger equation whose solution exhibits an initial weak singularity. A fully discrete scheme is constructed using L 1 scheme on gr...

In this paper, a new numerical scheme is constructed to solve a class of Infinite Horizon Optimal Control Problems (IHOCPs). The idea is to extend the spectral Ritz method to solve an IHOCP directl...

During the past decades, the general Klein–Gordon–Schrodinger systems have been playing more and more important roles in quantum mechanics. In this paper, the conservative Fourier pseudo-spectral s...

Alternating direction implicit (ADI) method is widely utilized and computationally efficient for numerical approximation of the multidimensional evolution equations. This paper mainly formulates an...

In this paper, the convergence for improved multi-point Chebyshev-like methods is considered. Compared to the results of Chebyshev method with second derivative in reference [M.A. Hernandez, M.A. S...

In this paper, we approximate the solution of Fredholm integro-differential equations of the second kind by using exponential spline function. The proposed method reduces to the system of a...

In this paper, by applying order reduction approach, a second-order accurate box scheme is established to solve a nonlinear delayed convection-diffusion equations with Neumann boundary conditions. ...

In this paper, by the relaxation technique, the relaxation modulus-based matrix splitting iteration method is presented for solving a class of nonlinear complementarity problems. The convergence co...

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 Pade 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...

In this paper, we introduce new type iterative scheme called a ‘modified Picard-S hybrid’ iterative algorithm to establish Δ-convergence and strong convergence theorems under suitable conditions fo...

This paper presents the finite difference scheme for the time-fractional Fokker–Planck equation with the external force and source term which depends on space and time. We prove the stability and c...

Based on the mixed finite element method, we consider the decoupled Crank–Nicolson/Adams–Bashforth scheme for the Boussinesq equations with smooth initial data in this paper. The temporal treatment...

An efficient second-order method for pricing European and American options under regime-switching jump-diffusion models is presented and analysed for stability and convergence. The implicit–explicit (IMEX) nature of the proposed method avoids the need to invert a full matrix and leads to tridiagonal systems that can be efficiently solved by direct methods. The IMEX predictor–corrector method is coupled with the operator splitting method to solve the linear complementarity problem of the American options. Numerical experiments are performed to demonstrate the stability and second-order convergence of the method.

In this article, a compact difference scheme is investigated to solve the Zakharov–Rubenchik equations in one dimension. The new scheme is proved to conserve the total mass and energy in the discre...

Pricing of European and American options under Bates model give rise to a partial integro-differential equation. In this paper a strongly stable fourth-order implicit predictor–corrector time stepping method based on exponential time differencing) is proposed for solving such problems. We provide stability, and convergence of the proposed method, and study the impact of the jump intensity, penalty and other parameters on convergence and solution accuracy. The American option constraint is enforced by using a penalty method. Spatial derivatives are approximated using second-order finite central differences which leads to block tridiagonal systems. The integral term is evaluated using simple quadrature where the non-locality of the jump term in such models leads to dense matrix. We treat the approximated integral term and nonlinear penalty term explicitly in time. Numerical experiments are demonstrated by discussing the efficiency, accuracy and reliability of the proposed method.

In this work, we consider a system of weakly coupled semi-linear parabolic equations of optimal portfolio in a regime-switching model in the case of exponential utility function, suggested by A.R. ...

We report a new algorithm for solving linear parabolic partial differential equations in two space dimension. The algorithm employs optimal biquadratic spline collocation for space discretization a...