Error estimate for the numerical solution of fractional reaction–subdiffusion process based on a meshless method

Abstract

In this paper a numerical technique based on a meshless method is proposed for solving the time fractional reaction–subdiffusion equation. Firstly, we obtain a time discrete scheme based on a finite difference scheme, then we use the meshless Galerkin method, to approximate the spatial derivatives and obtain a full discrete scheme. In the proposed scheme, some integrals appear over the boundary and the domain of problem which will be approximated using Gauss–Legendre quadrature rule. Then, we prove that the time discrete scheme is unconditionally stable and convergent using the energy method. We show convergence order of the time discrete scheme is O(τγ). The aim of this paper is to obtain an error estimate and to show convergence for the meshless Galerkin method based on the radial basis functions. Numerical examples confirm the efficiency and accuracy of the proposed scheme.