Modified implicit fractional difference scheme for 2D modified anomalous fractional sub-diffusion equation

Abstract

Abstract In this paper, we solve two-dimensional modified anomalous fractional sub-diffusion equation using modified implicit finite difference approximation. The stability and convergence of the proposed scheme are analyzed by the Fourier series method. We show that the scheme is unconditionally stable and the approximate solution converges to the exact solution. A numerical example is given to show the application and feasibility of the proposed scheme.

Keywords

• modified anomalous fractional sub-diffusion equation
• modified implicit difference method
• stability
• convergence