In this article, a numerical study for the fractional wave equations is introduced by using a class of finite difference methods. These methods are extension of the weighted average methods for ordinary (non-fractional) wave equations. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. Simple and ...

In this article, a high order implicit compact difference method for the fractional reaction-subdiffusion equation is presented. The difference scheme is unconditionally stable and the truncation error is of first order in time and forth order in space. A numerical example is included to demonstrate the validity of theoretical results and efficiency of the scheme.

Various fields of science and engineering deal with dynamical systems that can be described by fractional partial differential equations (FPDE), for example, systems biology, chemistry and biochemistry applications due to anomalous diffusion effects in constrained environments. However, effective numerical methods and numerical analysis for FPDE are still in their infancy. In this paper, we con...

This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N) for storing the dense or even full matrices that arise from application of numerical methods and how to manage the...

In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference schem...

Article history: Received 30 March 2013 Received in revised form 21 July 2013 Accepted 5 February 2014 Available online 14 February 2014

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are discussed. Introduction The Black-Scholes-Merton model for option prices is an ...

In this paper, a mixed matrix transform method with fractional centered difference scheme for solving diffusion equation Riesz derivative was examined. It obtained that the numerical unconditionally stable and feasible using analysis method. Numerical experiments were, then, carried out to support theoretical predictions.

In this work we construct and analyze discrete artificial boundary conditions (ABCs) for different finite difference schemes to solve nonlinear Schrödinger equations. These new discrete boundary conditions are motivated by the continuous ABCs recently obtained by the potential strategy of Szeftel. Since these new nonlinear ABCs are based on the discrete ABCs for the linear problem we first revi...