Dynamical systems method for solving nonlinear equations with monotone operators

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.

19 pages, 4 figures, 4 tables

References in corpus (5)

• Dynamical Systems Gradient method for solving nonlinear equations with monotone operators
• Global convergence for ill-posed equations with monotone operators: the dynamical systems method
• Dynamical Systems Method for ill-posed equations with monotone operators
• A new discrepancy principle
• On the discrepancy principle

Cited by in corpus (3)

• Dynamical Systems Gradient method for solving nonlinear equations with monotone operators
• Dynamical Systems Method for solving nonlinear equations with locally Holder continuous monotone operators
• An iterative scheme for solving equations with locally $\sigma$-inverse monotone operators