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arXiv · 2510.27302

High-precision newton-kantorovich method for nonlinear integral equations

Kirill A. Chertoganov·Valery I. Shipalov
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Abstract

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.

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Kirill A. Chertoganov, Valery I. Shipalov. 2025-10-31. High-precision newton-kantorovich method for nonlinear integral equations. https://arxiv.org/abs/2510.27302

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