Gautschi-type and implicit-explicit integrators for constrained wave equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917070068776960 |
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| author | Altmann, R. Dörich, B. Zimmer, C. |
| author_facet | Altmann, R. Dörich, B. Zimmer, C. |
| contents | This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely, we consider an implicit-explicit Crank-Nicolson scheme as well as an exponential integrator of Gautschi type. For this, well-known wave integrators for unconstrained systems are combined with techniques known from the field of differential-algebraic equations. This results in efficient time stepping schemes that are provable of second order. Moreover, we discuss the practical implementation of the Gautschi-type method, which involves the solution of certain saddle point problems. The theoretical results are verified by a numerical experiment for the wave equation with kinetic boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gautschi-type and implicit-explicit integrators for constrained wave equations Altmann, R. Dörich, B. Zimmer, C. Numerical Analysis This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely, we consider an implicit-explicit Crank-Nicolson scheme as well as an exponential integrator of Gautschi type. For this, well-known wave integrators for unconstrained systems are combined with techniques known from the field of differential-algebraic equations. This results in efficient time stepping schemes that are provable of second order. Moreover, we discuss the practical implementation of the Gautschi-type method, which involves the solution of certain saddle point problems. The theoretical results are verified by a numerical experiment for the wave equation with kinetic boundary conditions. |
| title | Gautschi-type and implicit-explicit integrators for constrained wave equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.22532 |