An Integral Equation Method for Linear Two-Point Boundary Value Systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914080395100160 |
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| author | Zhang, Tianze Ma, Yixuan Wang, Jun |
| author_facet | Zhang, Tianze Ma, Yixuan Wang, Jun |
| contents | We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a well-conditioned integral equation. We then make use of a high-order Nystrom discretization and a fast direct solver on the continuous level to obtain a black-box solver that is fast and accurate. A numerical study of the conditioning of different integral formulations is carried out. Excellent performance in speed, accuracy, and robustness is demonstrated with several challenging numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Integral Equation Method for Linear Two-Point Boundary Value Systems Zhang, Tianze Ma, Yixuan Wang, Jun Numerical Analysis We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a well-conditioned integral equation. We then make use of a high-order Nystrom discretization and a fast direct solver on the continuous level to obtain a black-box solver that is fast and accurate. A numerical study of the conditioning of different integral formulations is carried out. Excellent performance in speed, accuracy, and robustness is demonstrated with several challenging numerical examples. |
| title | An Integral Equation Method for Linear Two-Point Boundary Value Systems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.06678 |