Numerical solution of fractional diffusion-wave equation based on fractional multistep method

Abstract

This paper is devoted to application of fractional multistep method in the numerical solution of fractional diffusion-wave equation. By transforming the diffusion-wave equation into an equivalent integro-differential equation and applying Lubich’s fractional multistep method of second order we obtain a scheme of order O(τα+h2) for 1⩽α⩽1.71832 where α is the order of temporal derivative and τ and h denote temporal and spatial stepsizes. The solvability, convergence and stability properties of the algorithm are investigated and numerical experiment is carried out to verify the feasibility of the scheme.