A high-order numerical algorithm for two-dimensional time–space tempered fractional diffusion-wave equation

Abstract

In this paper, we focus our attention on the development of the high-order numerical algorithm for the time–space tempered fractional diffusion-wave equation in two spatial dimensions. Based on the fourth-order fractional–compact difference operator, a new difference scheme with convergence order O(τ2+h14+h24) is derived, where τ is the temporal stepsize, h1 and h2 are the spatial stepsizes, respectively. The stability and convergence of the algorithm are investigated by the energy method and numerical experiment is carried out to verify the feasibility of the numerical algorithm.