A global approximation method for second-kind nonlinear integral equations

被引：0

作者：

Fermo, Luisa ^{[1
]}

Laguardia, Anna Lucia ^{[2
]}

Laurita, Concetta ^{[2
]}

Russo, Maria Grazia ^{[3
]}

机构：

[1] Univ Cagliari, Dept Math & Comp Sci, Via Osped 72, I-09124 Cagliari, Italy

[2] Univ Basilicata, Dept Basic & Appl Sci, Viale Ateneo Lucano 10, I-85100 Potenza, Italy

[3] Univ Basilicata, Dept Engn, Viale Ateneo Lucano 10, I-85100 Potenza, Italy

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2025年 / 487卷

关键词：

Nonlinear integral equations; Hammerstein-type integral equations; Nystr & ouml; m method; Boundary integral equations; BOUNDARY-VALUE-PROBLEMS; NUMERICAL-SOLUTION; HAMMERSTEIN EQUATIONS; PROJECTION METHODS; COLLOCATION METHOD; LAPLACE EQUATION; DOMAINS; FREDHOLM;

D O I：

10.1016/j.amc.2024.129094

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A global approximation method of Nystr & ouml;m type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first occurrence, the method uses a Gauss-Legendre rule whereas in the second one resorts to a product rule based on Legendre nodes. Stability and convergence are proved in functional spaces equipped with the uniform norm and several numerical tests are given to show the good performance of the proposed method. An application to the interior Neumann problem for the Laplace equation with nonlinear boundary conditions is also considered.

引用

页数：21

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