Du, RuilianYan, YubinLiang, Zongqi2018-10-312018-10-312018-10-05Du, R., Yan, Y. and Liang, Z., (2019). A high-order scheme to approximate the caputo fractional derivative and its application to solve the fractional diffusion wave equation, Journal of Computational Physics, 376, pp. 1312-13300021-999110.1016/j.jcp.2018.10.011http://hdl.handle.net/10034/621500A new high-order finite difference scheme to approximate the Caputo fractional derivative $\frac{1}{2} \big ( \, _{0}^{C}D^{\alpha}_{t}f(t_{k})+ \, _{0}^{C}D^{\alpha}_{t}f(t_{k-1}) \big ), k=1, 2, \dots, N, $ with the convergence order $O(\Delta t^{4-\alpha}), \, \alpha\in(1,2)$ is obtained when $f^{\prime \prime \prime} (t_{0})=0$, 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 $O(\Delta t^{4-\alpha} + h^2)$, where $h$ denotes the space step size. Numerical examples are given to show that the numerical results are consistent with the theoretical results.enhttps://creativecommons.org/licenses/by-nc-nd/3.0/Caputo fractional derivativefractional diffusion wave equationFinite difference methodArticleJournal of Computational Physics