Dynamical systems method for solving nonlinear equations with monotone operators

TL;DR

This paper introduces a Dynamical Systems Method (DSM) with an a posteriori stopping rule for efficiently solving ill-posed nonlinear equations involving monotone operators in Hilbert spaces, supported by numerical experiments.

Contribution

The paper develops a new DSM version with a mathematically justified stopping rule for monotone operator equations in Hilbert spaces.

Findings

DSM with stopping rule is numerically efficient

Effective for solving nonlinear integral equations

Validated through numerical experiments

Abstract

A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators in a Hilbert space is studied in this paper. An a posteriori stopping rule, based on a discrepancy-type principle is proposed and justified mathematically. The results of two numerical experiments are presented. They show that the proposed version of DSM is numerically efficient. The numerical experiments consist of solving nonlinear integral equations.