Dynamical systems method for solving nonlinear equations with locally Hölder continuous monotone operators

DOI10.1504/IJCSM.2010.033927zbMATH Open1197.65059arXiv1002.4162OpenAlexW2097550751MaRDI QIDQ988532

Nguyen Si Hoang

Publication date: 17 August 2010

Published in: International Journal of Computing Science and Mathematics (Search for Journal in Brave)

Abstract: A version of the Dynamical Systems Method for solving ill-posed nonlinear equations with monotone and locally H"{o}lder continuous operators is studied in this paper. A discrepancy principle is proposed and justified under natural and weak assumptions. The only smoothness assumption on $F$ is the local H"{o}lder continuity of order $alpha>1/2$.

Full work available at URL: https://arxiv.org/abs/1002.4162

zbMATH Keywords

stabilityconvergenceHilbert spacemonotone operatorsnonlinear operator equationsill-posed nonlinear equationsdynamical systems method

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

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