Convergence Rate of Runge-Kutta-Type Regularization for Nonlinear Ill-Posed Problems under Logarithmic Source Condition

Convergence Rate of Runge-Kutta-Type Regularization for Nonlinear Ill-Posed Problems under Logarithmic Source Condition

We 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...

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Bibliographic Details
Main Authors: Pornsarp Pornsawad, Elena Resmerita, Christine Böckmann
Format: Article
Language:English
Published: MDPI AG 2021-05-01
Series:Mathematics
Subjects:
nonlinear inverse problem
ill-posed problem
iterative regularization
Runge-Kutta methods
logarithmic source condition
discrepancy principle
Online Access:https://www.mdpi.com/2227-7390/9/9/1042

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