Efficient computation of the sinc matrix function for the integration of second-order differential equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914992466427904 |
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| author | Aceto, Lidia Durastante, Fabio |
| author_facet | Aceto, Lidia Durastante, Fabio |
| contents | This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit (pronounced or highly) oscillatory behavior, standard numerical methods are known to perform poorly. Our approach consists in directly discretizing the problem by means of Gautschi-type integrators based on $\operatorname{sinc}$ matrix functions. The novelty contained here is that of using a suitable rational approximation formula for the $\operatorname{sinc}$ matrix function to apply a rational Krylov-like approximation method with suitable choices of poles. In particular, we discuss the application of the whole strategy to a finite element discretization of the wave equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09676 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient computation of the sinc matrix function for the integration of second-order differential equations Aceto, Lidia Durastante, Fabio Numerical Analysis 65L06, 15A16, 41A20 This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit (pronounced or highly) oscillatory behavior, standard numerical methods are known to perform poorly. Our approach consists in directly discretizing the problem by means of Gautschi-type integrators based on $\operatorname{sinc}$ matrix functions. The novelty contained here is that of using a suitable rational approximation formula for the $\operatorname{sinc}$ matrix function to apply a rational Krylov-like approximation method with suitable choices of poles. In particular, we discuss the application of the whole strategy to a finite element discretization of the wave equation. |
| title | Efficient computation of the sinc matrix function for the integration of second-order differential equations |
| topic | Numerical Analysis 65L06, 15A16, 41A20 |
| url | https://arxiv.org/abs/2304.09676 |