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

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(tau(alpha) + h(2)) for 1 <= alpha <= 1.71832 where a is the order of temporal derivative and tau 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. Crown Copyright (C) 2014 Published by Elsevier Inc. All rights reserved.