Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems

Abstract

ABSTRACTThis work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under a Hölder-type sourcewise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt, Lobatto, and Radau methods.