Abstract
In this paper, the H 2 N 2 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 − γ . 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 ( τ 3 − γ + h 4 + ϵ ) , where K 1 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.
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