A fast compact finite difference scheme for the fourth-order diffusion-wave equation

In this paper, the H2N2 method and compact finite difference scheme are proposed for the fourth-order time-fractional diffusion-wave equations. In order to improve the efficiency of calculation, a fast scheme is constructed with utilizing the sum-of-exponentials to approximate the kernel t(1-gamma). Based on the discrete energy method, the Cholesky decomposition method and the reduced-order method, we prove the stability and convergence. When K-1 < 3/2, the convergence order is O(tau(3-gamma) + h(4) + epsilon), where K-1 is diffusion coefficient, gamma is the order of fractional derivative, tau is the parameters for the time meshes, h is the parameters for the space meshes and epsilon is tolerance error. Numerical results further verify the theoretical analysis. It is find that the CPU time is extremely little in our scheme.