Stability and Convergence of Explicit Difference Method for Solving the 3-Dimensional Two-Sided Fractional Diffusion Equation

Abstract

In this paper, a numerical solution of the 3-dimensional two-sided fractionaldiffusion equation has been presented. The algorithm for the numerical solution forthis equation is based on explicit finite difference method. The consistency, conditionalstability, and convergence of the fractional order numerical method are described.The numerical method has been applied to solve a practical numerical example andthe results have been compared with exact solution. The results were presented intables using the MathCAD 12 software package when it is needed. The explicit finitedifference method appeared to be effective and reliable in solving the 3-dimensionaltwo-sided fractional Diffusion equation