A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation

A new high-order finite difference scheme to approximate the Caputo fractional derivative 1/2(C 0 D(t)(proportional to )f (t(k)) + C 0 D(t)(proportional to )f (t(k)(-1))) , k = 1, 2, ..., N, with the convergence order 0 (Delta t(4-proportional to)), proportional to is an element of (1, 2) is obtained when f'''(t(0)) = 0, where Delta t denotes the time step size. Based on this scheme we introduce a finite difference method for solving fractional diffusion wave equation with the convergence order 0(Delta t(4-proportional to)+ h(2)), where h denotes the space step size. Numerical examples are given to show that the numerical results are consistent with the theoretical results. (C) 2018 Elsevier Inc. All rights reserved.