Convergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source condition

Pornsarp PornsawadElena ResmeritaChristine BöckmannInstitut für Mathematik der Universität PotsdamAlfred-Wegener-Institut Helmholtz-Zentrum für Polar- und MeeresforschungAlpen-Adria-Universität KlagenfurtSilpakorn UniversityMahidol University2022-08-042022-08-042021-05-01Mathematics. Vol.9, No.9 (2021)222773902-s2.0-85106178137https://repository.li.mahidol.ac.th/handle/123456789/77380We prove the logarithmic convergence rate of the families of usual and modified iterative Runge–Kutta methods for nonlinear ill-posed problems between Hilbert spaces under the logarithmic source condition, and numerically verify the obtained results. The iterative regularization is terminated by the a posteriori discrepancy principle.Mahidol UniversityMathematicsConvergence rate of runge–kutta-type regularization for nonlinear ill-posed problems under logarithmic source conditionArticleSCOPUS10.3390/math9091042