Dynamical systems method for solving nonlinear equations with monotone operators
For researchers working on ill-posed nonlinear problems, this provides a theoretically justified stopping rule for DSM, though it is an incremental improvement.
The paper presents a version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators, including a justified a posteriori stopping rule. Numerical experiments on nonlinear integral equations demonstrate efficiency.
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.