Numerical Methods for Fractional Reaction-Dispersion Equation with Riesz Space Fractional Derivative

Abstract

In this paper, a numerical solution of fractional reaction-dispersion equation with Riesz space fractional derivative has been presented. The algorithm for the numerical solution for this equation is based on two finite difference methods. The consistency, stability, and convergence of the fractional order numerical method are described. The numerical methods have been applied to solve a practical numerical example and comparing results with the exact solution. The results were presented in tables using the MathCAD 12 software package when it is needed. The two finite difference methods appeared to be effective and reliable in solving fractional reaction-dispersion equation with Riesz space fractional derivative.

Keywords

• riesz fractional derivative
• two finite difference methods
• fractional reaction
• dispersion equation
• stability
• convergence