On the numerical solution and convergence study for the system of nonlinear fractional diffusion equations

Abstract

In this article, an implementation of an efficient numerical method for solving the system of coupled nonlinear fractional diffusion equations (NFDEs) is introduced. The proposed system has many applications, such as porous media and plasma transport. The fractional derivative is described in the Caputo sense. The method is based upon a combination between the properties of the Legendre approximations and finite difference method (FDM). The proposed method reduces NFDEs to a system of ordinary differential equations that are solved using FDM. Special attention is given to the study of the convergence analysis and deducing the upper bound of the error of the resulting approximate solution. A numerical example is given to show the validity and the accuracy of the proposed method.