Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908656033857536 |
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| author | Bleecke, Sebastian Biswas, Abhijit Ketcheson, David I. Ranocha, Hendrik Schutz, Jochen |
| author_facet | Bleecke, Sebastian Biswas, Abhijit Ketcheson, David I. Ranocha, Hendrik Schutz, Jochen |
| contents | We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods using implicit-explicit (additive) Runge-Kutta methods that are implicit in the stiff linear part. The new discretization of the hyperbolization conserves important invariants converging to invariants of the BBM equation. We use the entropy relaxation approach to make the fully discrete schemes energy-preserving. Numerical experiments demonstrate the effectiveness of these discretizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation Bleecke, Sebastian Biswas, Abhijit Ketcheson, David I. Ranocha, Hendrik Schutz, Jochen Numerical Analysis Pattern Formation and Solitons We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods using implicit-explicit (additive) Runge-Kutta methods that are implicit in the stiff linear part. The new discretization of the hyperbolization conserves important invariants converging to invariants of the BBM equation. We use the entropy relaxation approach to make the fully discrete schemes energy-preserving. Numerical experiments demonstrate the effectiveness of these discretizations. |
| title | Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation |
| topic | Numerical Analysis Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2511.10044 |