Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910946559000576 |
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| author | Ketcheson, David I. Biswas, Abhijit |
| author_facet | Ketcheson, David I. Biswas, Abhijit |
| contents | We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are potentially useful as either analytical or computational tools for understanding the corresponding higher-order equation. We perform a systematic analysis of a family of linear model equations and show that for each member of this family there is a stable hyperbolic approximation whose solution converges to that of the model equation in a certain limit. We then show through several examples that this approach can be applied successfully to a very wide range of nonlinear PDEs of practical interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation Ketcheson, David I. Biswas, Abhijit Analysis of PDEs Numerical Analysis We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are potentially useful as either analytical or computational tools for understanding the corresponding higher-order equation. We perform a systematic analysis of a family of linear model equations and show that for each member of this family there is a stable hyperbolic approximation whose solution converges to that of the model equation in a certain limit. We then show through several examples that this approach can be applied successfully to a very wide range of nonlinear PDEs of practical interest. |
| title | Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2405.16841 |