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

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  • Pornsarp Pornsawad

    (Department of Mathematics, Faculty of Science, Silpakorn University, 6 Rachamakka Nai Rd., Nakhon Pathom 73000, Thailand
    Centre of Excellence in Mathematics, Mahidol University, Rama 6 Rd., Bangkok 10400, Thailand)

  • Elena Resmerita

    (Institute of Mathematics, Alpen-Adria University of Klagenfurt, Universitätsstr. 65-67, A-9020 Klagenfurt, Austria)

  • Christine Böckmann

    (Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany
    Helmholtz Centre for Polar and Marine Research, Alfred Wegener Institute, Telegrafenberg A45, 14473 Potsdam, Germany)

Abstract

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 a posteriori discrepancy principle.

Suggested Citation

  • Pornsarp Pornsawad & Elena Resmerita & Christine Böckmann, 2021. "Convergence Rate of Runge-Kutta-Type Regularization for Nonlinear Ill-Posed Problems under Logarithmic Source Condition," Mathematics, MDPI, vol. 9(9), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1042-:d:548733
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    References listed on IDEAS

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    1. Pornsarp Pornsawad & Nantawan Sapsakul & Christine Böckmann, 2019. "A Modified Asymptotical Regularization of Nonlinear Ill-Posed Problems," Mathematics, MDPI, vol. 7(5), pages 1-19, May.
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