Stability for discrete time waveform relaxation methods based on Euler schemes
Stability properties of discrete time waveform relaxation (DWR) methods based on Euler schemes are analyzed by applying them to two dissipative systems. Some sufficient conditions for stability of the considered methods are obtained; at the same time two examples of instability are given. To investi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231206?viewType=HTML |
| _version_ | 1797742994801033216 |
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| author | Junjiang Lai Zhencheng Fan |
| author_facet | Junjiang Lai Zhencheng Fan |
| author_sort | Junjiang Lai |
| collection | DOAJ |
| description | Stability properties of discrete time waveform relaxation (DWR) methods based on Euler schemes are analyzed by applying them to two dissipative systems. Some sufficient conditions for stability of the considered methods are obtained; at the same time two examples of instability are given. To investigate the influence of the splitting functions and underlying numerical methods on stability of DWR methods, DWR methods based on different splittings and different numerical schemes are considered. The obtained results show that the stabilities of waveform relaxation methods based on an implicit Euler scheme are better than those based on explicit Euler scheme, and that the stabilities of waveform relaxation methods based on the classical splittings such as Gauss-Jacobi and Gauss-Seidel splittings are worse than those based on the eigenvalue splitting presented in this paper. Finally, numerical examples that confirm the theoretical results are presented. |
| first_indexed | 2024-03-12T14:48:12Z |
| format | Article |
| id | doaj.art-c7de92a0f3664dadb493f51d38bc6247 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T14:48:12Z |
| publishDate | 2023-08-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-c7de92a0f3664dadb493f51d38bc62472023-08-16T01:30:15ZengAIMS PressAIMS Mathematics2473-69882023-08-01810237132373310.3934/math.20231206Stability for discrete time waveform relaxation methods based on Euler schemesJunjiang Lai0Zhencheng Fan 1College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, ChinaCollege of Mathematics and Data Science, Minjiang University, Fuzhou 350108, ChinaStability properties of discrete time waveform relaxation (DWR) methods based on Euler schemes are analyzed by applying them to two dissipative systems. Some sufficient conditions for stability of the considered methods are obtained; at the same time two examples of instability are given. To investigate the influence of the splitting functions and underlying numerical methods on stability of DWR methods, DWR methods based on different splittings and different numerical schemes are considered. The obtained results show that the stabilities of waveform relaxation methods based on an implicit Euler scheme are better than those based on explicit Euler scheme, and that the stabilities of waveform relaxation methods based on the classical splittings such as Gauss-Jacobi and Gauss-Seidel splittings are worse than those based on the eigenvalue splitting presented in this paper. Finally, numerical examples that confirm the theoretical results are presented.https://www.aimspress.com/article/doi/10.3934/math.20231206?viewType=HTMLstabilitydiscrete time waveform relaxation methodseuler methodsordinary differential equations |
| spellingShingle | Junjiang Lai Zhencheng Fan Stability for discrete time waveform relaxation methods based on Euler schemes AIMS Mathematics stability discrete time waveform relaxation methods euler methods ordinary differential equations |
| title | Stability for discrete time waveform relaxation methods based on Euler schemes |
| title_full | Stability for discrete time waveform relaxation methods based on Euler schemes |
| title_fullStr | Stability for discrete time waveform relaxation methods based on Euler schemes |
| title_full_unstemmed | Stability for discrete time waveform relaxation methods based on Euler schemes |
| title_short | Stability for discrete time waveform relaxation methods based on Euler schemes |
| title_sort | stability for discrete time waveform relaxation methods based on euler schemes |
| topic | stability discrete time waveform relaxation methods euler methods ordinary differential equations |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231206?viewType=HTML |
| work_keys_str_mv | AT junjianglai stabilityfordiscretetimewaveformrelaxationmethodsbasedoneulerschemes AT zhenchengfan stabilityfordiscretetimewaveformrelaxationmethodsbasedoneulerschemes |