Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911800151244800 |
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| author | Doehring, Daniel Gassner, Gregor J. Torrilhon, Manuel |
| author_facet | Doehring, Daniel Gassner, Gregor J. Torrilhon, Manuel |
| contents | A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach allows the optimization of stability polynomials with more than hundred stages. A potential application of these high degree stability polynomials are problems with locally varying characteristic speeds as found in non-uniformly refined meshes and different wave speeds.
To demonstrate the applicability of the stability polynomials we construct 2N storage many-stage Runge-Kutta methods that match their designed second order of accuracy when applied to a range of linear and nonlinear hyperbolic PDEs with smooth solutions. The methods are constructed to reduce the amplification of round off errors which becomes a significant concern for these many-stage methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations Doehring, Daniel Gassner, Gregor J. Torrilhon, Manuel Numerical Analysis Mathematical Physics Classical Analysis and ODEs 65L06, 65M20 A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach allows the optimization of stability polynomials with more than hundred stages. A potential application of these high degree stability polynomials are problems with locally varying characteristic speeds as found in non-uniformly refined meshes and different wave speeds. To demonstrate the applicability of the stability polynomials we construct 2N storage many-stage Runge-Kutta methods that match their designed second order of accuracy when applied to a range of linear and nonlinear hyperbolic PDEs with smooth solutions. The methods are constructed to reduce the amplification of round off errors which becomes a significant concern for these many-stage methods. |
| title | Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations |
| topic | Numerical Analysis Mathematical Physics Classical Analysis and ODEs 65L06, 65M20 |
| url | https://arxiv.org/abs/2402.12140 |