Explicit Finite Difference Approximation for the TwoDimensional Fractional Dispersion Equation

Abstract

In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional dispersion equation. The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of this numerical method are described. Finally, numerical example is presented to show the dispersion behavior according to the order of the fractional derivative and we demonstrate that our explicit finite difference approximation is a computationally efficient method for solving two-dimensional fractional dispersion equation

Keywords

• Fractional derivative, Two-dimensional probem, Explicit Euler method, fractional dispersion equation, Stability, Convergence