A compact difference scheme for the fractional diffusion-wave equation

This article is devoted to the study of high order difference methods for the fractional diffusion-wave equation. The time fractional derivatives are described in the Caputo’s sense. A compact difference scheme is presented and analyzed. It is shown that the difference scheme is unconditionally convergent and stable in _L∞$L_{\infty }$-norm. The convergence order is O(τ^3-α+h⁴)$O({\tau }^{3-\alpha }+h^4)$. Two numerical examples are also given to demonstrate the theoretical results.