A Product Integration type Method for solving Nonlinear Integral Equations in L

TL;DR

This paper extends the product integration method to solve nonlinear Fredholm integral equations with weakly singular kernels in the L1 space, providing a new numerical approach for such equations.

Contribution

The paper introduces a novel extension of the product integration scheme from continuous to L1 spaces for nonlinear integral equations with singular kernels.

Findings

Successfully extended the product integration method to L1 space.

Demonstrated the method's effectiveness on weakly singular kernels.

Provides a new numerical tool for solving nonlinear Fredholm equations.

Abstract

This paper deals with nonlinear Fredholm integral equations of the second kind. We study the case of a weakly singular kernel and we set the problem in the space L 1 ([a, b], C). As numerical method, we extend the product integration scheme from C 0 ([a, b], C) to L 1 ([a, b], C).