Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition

Abstract

In this paper, a numerical method is proposed to solve the time-space fractional diffusion equation with Robin fractional derivative boundary condition. Under the weak regularity assumptions of solution, we present a numerical scheme based on the L1 method for time discretization on graded mesh and the Grunwald-Letnikov formula for spatial discretization on uniform mesh. And a fast scheme for the considered problem is constructed based on the exponential summation approximation of the kernel function t−α. Meanwhile, a detailed analysis of stability and convergence is given. Then, the extrapolation method is applied to the space direction to make it reach the second-order accuracy. Finally, numerical experiments show that the proposed method is effective.