An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

Lei Ren and Lei Liu

Advances in Mathematical Physics, 2019, vol. 2019, issue 1

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 2 − α 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 L2‐1σ 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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https://doi.org/10.1155/2019/3263589

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:3263589

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