Numerical solution of a certain type of integral equations on the real half-line

TL;DR

This paper introduces a numerical method for solving a specific class of nonlinear integral equations on the real half-line, proving convergence and approximation properties.

Contribution

The paper presents a new numerical approach for nonlinear integral equations with two integrals, including convergence proofs and finite truncation analysis.

Findings

Proves convergence and rate of convergence of the method

Establishes approximation results for finite truncations

Demonstrates effectiveness for equations on the half-line

Abstract

We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the convergence and the rate of convergence of our method. The discretization results in an infinite-dimensional nonlinear system, and we also prove results on the approximation of the solution of the infinite-dimensional system by solution of finite truncations.