Numerical Solution of Multiple Nonlinear Volterra Integral Equations

TL;DR

This paper presents a numerical discretization approach for solving complex nonlinear Volterra integral equations with multiple integrals, establishing theoretical guarantees for solution existence, uniqueness, and convergence rates.

Contribution

It introduces a novel discretization method for nonlinear Volterra equations with multiple integrals and provides rigorous proofs of solution properties and convergence behavior.

Findings

Proved existence and uniqueness of solutions.

Established convergence and error estimates for the numerical method.

Validated the method's effectiveness for complex integral equations.

Abstract

We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.