Exponential Runge-Kutta methods for parabolic equations with state-dependent delay
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915489141227520 |
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| author | Huang, Qiumei Ostermann, Alexander Zhong, Gangfan |
| author_facet | Huang, Qiumei Ostermann, Alexander Zhong, Gangfan |
| contents | The aim of this paper is to construct and analyze exponential Runge-Kutta methods for the temporal discretization of a class of semilinear parabolic problems with arbitrary state-dependent delay. First, the well-posedness of the problem is established. Subsequently, first and second order schemes are constructed. They are based on the explicit exponential Runge-Kutta methods, where the delayed solution is approximated by a continuous extension of the time discrete solution. Schemes of arbitrary order can be constructed using the methods of collocation type. The unique solvability and convergence of the proposed schemes are established. Finally, we discuss implementation issues and present some numerical experiments to illustrate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential Runge-Kutta methods for parabolic equations with state-dependent delay Huang, Qiumei Ostermann, Alexander Zhong, Gangfan Numerical Analysis 65M12, 65L06 The aim of this paper is to construct and analyze exponential Runge-Kutta methods for the temporal discretization of a class of semilinear parabolic problems with arbitrary state-dependent delay. First, the well-posedness of the problem is established. Subsequently, first and second order schemes are constructed. They are based on the explicit exponential Runge-Kutta methods, where the delayed solution is approximated by a continuous extension of the time discrete solution. Schemes of arbitrary order can be constructed using the methods of collocation type. The unique solvability and convergence of the proposed schemes are established. Finally, we discuss implementation issues and present some numerical experiments to illustrate our theoretical results. |
| title | Exponential Runge-Kutta methods for parabolic equations with state-dependent delay |
| topic | Numerical Analysis 65M12, 65L06 |
| url | https://arxiv.org/abs/2509.08902 |