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A second order difference method combined with time two-grid algorithm for two-dimensional time-fractional Fisher equation
Yang, Wenguang1; Wang, Zhibo1,2; Ou, Caixia3
2024-11
Source PublicationInternational Journal of Computer Mathematics
ISSN0020-7160
Volume101Issue:11Pages:1255-1269
Abstract

In this paper, a finite difference (FD) scheme based on time two-grid algorithm is proposed for solving the two-dimensional time-fractional Fisher equation (2D-TFFE). Firstly, the Caputo fractional derivative and the spatial derivative are discretized by the 𝐿⁢2−1𝜎 formula and the central difference formula, respectively. In order to improve the efficiency of computation, the time two-grid algorithm is then constructed. Secondly, based on the cut-off function technic, stability and convergence of the time two-grid FD scheme are obtained by the energy method, and the global convergence order is O⁢(𝜏2𝐹+𝜏4𝐶+ℎ2𝑥+ℎ2𝑦) (Formula presented.), where  𝜏𝐹  and  and 𝜏𝐶 represent time-step sizes on the fine and coarse grid, respectively, while ℎ𝑥 and ℎ𝑦 represent the space-step sizes. Finally, numerical experiments are presented to show the feasibility and efficiency of the algorithm.

KeywordCut-off Function Method Stability And Convergence Time Two-grid Algorithm Time-fractional Fisher Equation
DOI10.1080/00207160.2024.2389859
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:001290325600001
PublisherTAYLOR & FRANCIS LTD, 2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
Scopus ID2-s2.0-85201120990
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Citation statistics
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Corresponding AuthorWang, Zhibo
Affiliation1.School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, Guangdong, China
2.Center for Mathematics and Interdisciplinary Sciences, School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, Guangdong, China
3.Department of Mathematics, University of Macau, Macao
Recommended Citation
GB/T 7714
Yang, Wenguang,Wang, Zhibo,Ou, Caixia. A second order difference method combined with time two-grid algorithm for two-dimensional time-fractional Fisher equation[J]. International Journal of Computer Mathematics, 2024, 101(11), 1255-1269.
APA Yang, Wenguang., Wang, Zhibo., & Ou, Caixia (2024). A second order difference method combined with time two-grid algorithm for two-dimensional time-fractional Fisher equation. International Journal of Computer Mathematics, 101(11), 1255-1269.
MLA Yang, Wenguang,et al."A second order difference method combined with time two-grid algorithm for two-dimensional time-fractional Fisher equation".International Journal of Computer Mathematics 101.11(2024):1255-1269.
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