Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction
In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choice...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Mosul University
2013-09-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_163531_88c397a69b02817b0a72d2de9bca2622.pdf |
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| _version_ | 1850196639914917888 |
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| author | Ann Jalal Mohammed Al-Amr |
| author_facet | Ann Jalal Mohammed Al-Amr |
| author_sort | Ann Jalal |
| collection | DOAJ |
| description | In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for . We have found that the two schemes are unconditionally stable when , while the consistent scheme is stable under the conditions and when . Also, the lumped scheme is stable under the conditions and when . |
| format | Article |
| id | doaj-art-e9b627a4afde47c98e55aaf617f2cdf6 |
| institution | OA Journals |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2013-09-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-e9b627a4afde47c98e55aaf617f2cdf62025-08-20T02:13:24ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902013-09-0110311712810.33899/csmj.2013.163531163531Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible ReactionAnn Jalal0Mohammed Al-Amr1Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, IraqDepartment of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, IraqIn this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for . We have found that the two schemes are unconditionally stable when , while the consistent scheme is stable under the conditions and when . Also, the lumped scheme is stable under the conditions and when .https://csmj.mosuljournals.com/article_163531_88c397a69b02817b0a72d2de9bca2622.pdffinite element schemereaction-diffusion systemconsistent schemelumped scheme |
| spellingShingle | Ann Jalal Mohammed Al-Amr Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction Al-Rafidain Journal of Computer Sciences and Mathematics finite element scheme reaction-diffusion system consistent scheme lumped scheme |
| title | Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction |
| title_full | Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction |
| title_fullStr | Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction |
| title_full_unstemmed | Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction |
| title_short | Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction |
| title_sort | fourier stability analysis of two finite element schemes for reaction diffusion system with fast reversible reaction |
| topic | finite element scheme reaction-diffusion system consistent scheme lumped scheme |
| url | https://csmj.mosuljournals.com/article_163531_88c397a69b02817b0a72d2de9bca2622.pdf |
| work_keys_str_mv | AT annjalal fourierstabilityanalysisoftwofiniteelementschemesforreactiondiffusionsystemwithfastreversiblereaction AT mohammedalamr fourierstabilityanalysisoftwofiniteelementschemesforreactiondiffusionsystemwithfastreversiblereaction |