High-precision newton-kantorovich method for nonlinear integral equations
Numerical Analysis
2025-11-03 v1 Numerical Analysis
Probability
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.
Cite
@article{arxiv.2510.27302,
title = {High-precision newton-kantorovich method for nonlinear integral equations},
author = {Kirill A. Chertoganov and Valery I. Shipalov},
journal= {arXiv preprint arXiv:2510.27302},
year = {2025}
}