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 t1−γ. Based on the discrete energy method, the Cholesky decomposition method and the reduced-order method, we prove the stability and convergence. When K1<32, the convergence order is O(τ3−γ+h4+ϵ), where K1 is diffusion coefficient, γ is the order of fractional derivative, τ is the parameters for the time meshes, h is the parameters for the space meshes and ε is tolerance error. Numerical results further verify the theoretical analysis. It is find that the CPU time is extremely little in our scheme.