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An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

Lei Ren () and Lei Liu ()

Advances in Mathematical Physics, 2019, vol. 2019, 1-9

Abstract: In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the - approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results.

Date: 2019
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DOI: 10.1155/2019/3263589

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