Mathematics

An iterative algorithm for solving nonlinear integral equations

B. A. Zaytsev, M. Yu. Medvedik

Penza State University, Penza

Abstract: Background. The purpose of this study is to develop an effective algorithm for solving nonlinear integral equations. Materials and methods. The method is based on the application of the principle of contraction mappings. The paper presents a description of the method and its justification. Results. The application of the method to various problems is considered, numerical results of solving integral equations are presented, showing the convergence of the method. Conclusions. The solution of test problems is given for various nonlinearity parameters, which allows us to draw a conclusion about the quality of the proposed method.

Keywords: nonlinear integral equation, principle of compressive maps, numerical method, mathematical model

UDC: 517.3

DOI: 10.21685/2072-3040-2025-3-4