High-order compact operator splitting method for three-dimensional fractional equation with subdiffusion

Abstract

In this paper, a high-order compact finite difference method is proposed to solve the three-dimensional (3D) time fractional convection–diffusion equation with subdiffusion (0<α<1). After a transform of the original problem, a difference scheme which is combined the Padé approximation for the space derivatives with the classical backward differentiation formula for time fractional derivative is presented. The new scheme is fourth-order accurate in space and (2-α)-order accurate in time. To increase the efficiency and stability of numerical solutions, the alternating direction implicit (ADI) operator splitting approach is employed. The stability analysis shows that this method is unconditionally stable. Numerical experiments are carried out to support the theoretical results.