High-precision newton-kantorovich method for nonlinear integral equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911243098390528 |
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| author | Chertoganov, Kirill A. Shipalov, Valery I. |
| author_facet | Chertoganov, Kirill A. Shipalov, Valery I. |
| contents | The paper considers the numerical solution of nonlinear integral equations using the Newton-Kantorovich method with the mpmath library. High-precision quadrature of the kernel K(t, s, u) with respect to the variable s for fixed t increases stability and accuracy in problems sensitive to rounding and dispersion. The presented implementation surpasses traditional low-precision methods, especially for strongly nonlinear kernels and stiff regimes, thereby expanding the applicability of the method in scientific and engineering computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-precision newton-kantorovich method for nonlinear integral equations Chertoganov, Kirill A. Shipalov, Valery I. Numerical Analysis Probability The paper considers the numerical solution of nonlinear integral equations using the Newton-Kantorovich method with the mpmath library. High-precision quadrature of the kernel K(t, s, u) with respect to the variable s for fixed t increases stability and accuracy in problems sensitive to rounding and dispersion. The presented implementation surpasses traditional low-precision methods, especially for strongly nonlinear kernels and stiff regimes, thereby expanding the applicability of the method in scientific and engineering computations. |
| title | High-precision newton-kantorovich method for nonlinear integral equations |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2510.27302 |