Implicit-explicit time discretization schemes for a class of semilinear wave equations with nonautonomous dampings
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914993300045824 |
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| author | Jiao, Zhe Li, Yaxu Zhao, Lijing |
| author_facet | Jiao, Zhe Li, Yaxu Zhao, Lijing |
| contents | This paper is concerned about the implicit-explicit (IMEX) methods for a class of dissipative wave systems with time-varying velocity feedbacks and nonlinear potential energies, equipped with different boundary conditions. Firstly, we approximate the problems by using a vanilla IMEX method, which is a second-order scheme for the problems when the damping terms are time-independent. However, rigors analysis shows that the error rate declines from second to first order due to the nonautonomous dampings. To recover the convergence order, we propose a revised IMEX scheme and apply it to the nonautonomous wave equations with a kinetic boundary condition. Our numerical experiments demonstrate that the revised scheme can not only achieve second-order accuracy but also improve the computational efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Implicit-explicit time discretization schemes for a class of semilinear wave equations with nonautonomous dampings Jiao, Zhe Li, Yaxu Zhao, Lijing Numerical Analysis 65M12, 65M15, 65J08 This paper is concerned about the implicit-explicit (IMEX) methods for a class of dissipative wave systems with time-varying velocity feedbacks and nonlinear potential energies, equipped with different boundary conditions. Firstly, we approximate the problems by using a vanilla IMEX method, which is a second-order scheme for the problems when the damping terms are time-independent. However, rigors analysis shows that the error rate declines from second to first order due to the nonautonomous dampings. To recover the convergence order, we propose a revised IMEX scheme and apply it to the nonautonomous wave equations with a kinetic boundary condition. Our numerical experiments demonstrate that the revised scheme can not only achieve second-order accuracy but also improve the computational efficiency. |
| title | Implicit-explicit time discretization schemes for a class of semilinear wave equations with nonautonomous dampings |
| topic | Numerical Analysis 65M12, 65M15, 65J08 |
| url | https://arxiv.org/abs/2410.20784 |