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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 2, Pages 215–222
DOI: https://doi.org/10.15372/SJNM20170208 (Mi sjvm647) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Discrete maximum-norm stability of a linearized second order finite difference scheme for Allen–Cahn equation

T. Hou, K. Wang, Y. Xiong, X. Xiao, Sh. Zhang

School of Mathematics and Statistics, Beihua University, Jilin, 132013, China
Full-text PDF (458 kB) Citations (11)
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DOI: https://doi.org/10.15372/SJNM20170208
Abstract: In this paper, we use finite difference methods for solving the Allen–Cahn equation which contains small perturbation parameters and strong nonlinearity. We consider a linearized second-order three level scheme in time and a second-order finite difference approach in space, and we establish discrete boundedness stability in maximum norm: if the initial data is bounded by 1, then the numerical solutions in later times can also be bounded uniformly by 1. We will show that the main result can be obtained under certain.
Key words: Allen–Cahn equation, finite difference method, discrete boundedness stability, maximum norm.
Funding agency Grant number
National Natural Science Foundation of China 11526036
11601014
Natural Science Foundation of Jilin Province 20160520108JH
Department of Education of Jilin Province 201646
Received: 02.05.2016
Revised: 08.10.2016
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 2, Pages 177–183
DOI: https://doi.org/10.1134/S1995423917020082
Bibliographic databases:
Document Type: Article
MSC: 49M25, 65M06
Language: Russian
Citation: T. Hou, K. Wang, Y. Xiong, X. Xiao, Sh. Zhang, “Discrete maximum-norm stability of a linearized second order finite difference scheme for Allen–Cahn equation”, Sib. Zh. Vychisl. Mat., 20:2 (2017), 215–222; Num. Anal. Appl., 10:2 (2017), 177–183
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
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