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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2024, Volume 27, Number 4, Pages 379–391
DOI: https://doi.org/10.15372/SJNM20240402 (Mi sjvm884) 		 
A linear second-order finite difference scheme for the Allen-Cahn equation with a general mobility

Z. Du, T. Hou

School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin, China
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DOI: https://doi.org/10.15372/SJNM20240402
Abstract: In this paper, a linear second-order finite difference scheme is proposed for the Allen-Cahn equation with a general positive mobility. The Crank-Nicolson scheme and Taylor's formula are used for temporal discretization, and the central finite difference method is used for spatial approximation. The discrete maximum bound principle (MBP), the discrete energy stability and $L^\infty$-norm error estimation are discussed, respectively. Finally, some numerical examples are presented to verify our theoretical results.
Key words: Allen-Cahn equation, general mobility, maximum bound principle, energy stability, error estimate.
Funding agency Grant number
Natural Science Foundation of Jilin Province 20230101279JC
This work is supported by the Science and Technology Research Project of Jilin Provincial Department of Education (grant no. JJKH20240076KJ) and the Natural Science Foundation of Jilin Province (grant no. 20230101279JC).
Received: 17.01.2024
Revised: 02.05.2024
Accepted: 26.08.2024
English version:
Numerical Analysis and Applications, 2024, Volume 17, Issue 4, Pages 313–325
DOI: https://doi.org/10.1134/S1995423924040025
Bibliographic databases:
Document Type: Article
MSC: 65M06, 65M15, 41A05, 41A25
Language: Russian
Citation: Z. Du, T. Hou, “A linear second-order finite difference scheme for the Allen-Cahn equation with a general mobility”, Sib. Zh. Vychisl. Mat., 27:4 (2024), 379–391; Num. Anal. Appl., 17:4 (2024), 313–325
Citation in format AMSBIB
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\by Z.~Du, T.~Hou
\paper A linear second-order finite difference scheme for the Allen-Cahn equation with a general mobility
\jour Sib. Zh. Vychisl. Mat.
\yr 2024
\vol 27
\issue 4
\pages 379--391
\mathnet{http://mi.mathnet.ru/sjvm884}
\crossref{https://doi.org/10.15372/SJNM20240402}
\edn{https://elibrary.ru/JKLXIO}
\transl
\jour Num. Anal. Appl.
\yr 2024
\vol 17
\issue 4
\pages 313--325
\crossref{https://doi.org/10.1134/S1995423924040025}
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