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Research Article | Open Access

High order compact difference scheme for solving the time multi-term fractional sub-diffusion equations

School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China
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Abstract

In this paper, a high order compact finite difference is established for the time multi-term fractional sub-diffusion equation. The derived numerical differential formula can achieve second order accuracy in time and four order accuracy in space. A unconditionally stable and convergent difference scheme is presented, and a rigorous proof for the stability and convergence is given. Numerical results demonstrate the efficiency of the proposed difference schemes.

Keywords

fractional sub-diffusion equationmulti-term fractional derivativesvariable coefficientcompact difference methodconvergencestability
CLC number: 65M06, 65M12, 65M15, 35R11

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 9172-9188
DOI: 10.3934/math.2022508

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Cite this article:
Ren L. High order compact difference scheme for solving the time multi-term fractional sub-diffusion equations. AIMS Mathematics, 2022, 7(5): 9172-9188. https://doi.org/10.3934/math.2022508

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Received: 28 December 2021
Revised: 18 February 2022
Accepted: 24 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)