Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach
The keys to constructing numerical schemes for nonlinear partial differential equations are accuracy, handling of the nonlinear terms, and physical properties (energy dissipation or conservation). In this paper, we employ the exponential scalar auxiliary variable (E-SAV) method to solve a semi-linea...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-07-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024200?viewType=HTML |
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| author | Huanhuan Li Lei Kang Meng Li Xianbing Luo Shuwen Xiang |
| author_facet | Huanhuan Li Lei Kang Meng Li Xianbing Luo Shuwen Xiang |
| author_sort | Huanhuan Li |
| collection | DOAJ |
| description | The keys to constructing numerical schemes for nonlinear partial differential equations are accuracy, handling of the nonlinear terms, and physical properties (energy dissipation or conservation). In this paper, we employ the exponential scalar auxiliary variable (E-SAV) method to solve a semi-linear wave equation. By defining two different variables and combining the Crank−Nicolson scheme, two semi-discrete schemes are proposed, both of which are second-order and maintain Hamiltonian conservation. Two numerical experiments are presented to verify the reliability of the theory. |
| format | Article |
| id | doaj-art-fd759c2d25a2492eb4d750a6dc9dd290 |
| institution | OA Journals |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-fd759c2d25a2492eb4d750a6dc9dd2902025-08-20T01:54:31ZengAIMS PressElectronic Research Archive2688-15942024-07-013274433445310.3934/era.2024200Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approachHuanhuan Li 0Lei Kang 1Meng Li 2 Xianbing Luo3Shuwen Xiang4School of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaThe keys to constructing numerical schemes for nonlinear partial differential equations are accuracy, handling of the nonlinear terms, and physical properties (energy dissipation or conservation). In this paper, we employ the exponential scalar auxiliary variable (E-SAV) method to solve a semi-linear wave equation. By defining two different variables and combining the Crank−Nicolson scheme, two semi-discrete schemes are proposed, both of which are second-order and maintain Hamiltonian conservation. Two numerical experiments are presented to verify the reliability of the theory.https://www.aimspress.com/article/doi/10.3934/era.2024200?viewType=HTMLsemi-linear wave equationexponential scalar auxiliary variableerror analysiscrank−nicolson scheme |
| spellingShingle | Huanhuan Li Lei Kang Meng Li Xianbing Luo Shuwen Xiang Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach Electronic Research Archive semi-linear wave equation exponential scalar auxiliary variable error analysis crank−nicolson scheme |
| title | Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach |
| title_full | Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach |
| title_fullStr | Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach |
| title_full_unstemmed | Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach |
| title_short | Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach |
| title_sort | hamiltonian conserved crank nicolson schemes for a semi linear wave equation based on the exponential scalar auxiliary variables approach |
| topic | semi-linear wave equation exponential scalar auxiliary variable error analysis crank−nicolson scheme |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024200?viewType=HTML |
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