Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems |
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| Authors: | Pornsarp Pornsawad Christine Böckmann |
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| Affiliation: | 1. Department of Mathematics, Faculty of Science, Silpakorn University, Nakorn Pathom, Thailandpornsawad_p@su.ac.th;3. Institute of Mathematics, University of Potsdam, Potsdam, Germany |
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| Abstract: | This 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. |
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| Keywords: | Nonlinear ill-posed problems Runge-Kutta methods regularization methods Hölder-type source condition stopping rules |
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