Long-time behavior of multi-step Finite Difference schemes with boundary via steepest descent and analytic combinatorics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914414436810752 |
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| author | Bellotti, Thomas Tenna, Tommaso |
| author_facet | Bellotti, Thomas Tenna, Tommaso |
| contents | We demonstrate how steepest descent arguments and singularity analysis from analytic combinatorics allow for an accurate description of the behavior of linear numerical schemes -- including the notorious leap-frog scheme -- in presence of stable and unstable boundary conditions in the long-time limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21899 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-time behavior of multi-step Finite Difference schemes with boundary via steepest descent and analytic combinatorics Bellotti, Thomas Tenna, Tommaso Numerical Analysis We demonstrate how steepest descent arguments and singularity analysis from analytic combinatorics allow for an accurate description of the behavior of linear numerical schemes -- including the notorious leap-frog scheme -- in presence of stable and unstable boundary conditions in the long-time limit. |
| title | Long-time behavior of multi-step Finite Difference schemes with boundary via steepest descent and analytic combinatorics |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.21899 |