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On the Consistency and Convergence of Repeated Richardson Extrapolation

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Numerical Methods and Applications (NMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13858))

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Abstract

Richardson extrapolation is a sequence acceleration method, which has long been used to enhance the accuracy of time integration methods for solving differential equations. Its classical version is based on a suitable linear combination of numerical solutions obtained by the same numerical method with two different discretization parameters. We present the principle of Richardson extrapolation, and introduce a possible generalization of this method called repeated Richardson extrapolation (RRE). The consistency and convergence of the new method obtained by combining certain Runge-Kutta methods with RRE are analysed and illustrated with numerical experiments.

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References

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Acknowledgements

We appreciate Zahari Zlatev’s useful advice during our investigation of the RRE method. The project has been supported by the Hungarian Scientific Research Fund OTKA SNN125119 and also OTKA K137699.

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Authors and Affiliations

  1. ELTE Eötvös Loránd University, Pázmány Péter s. 1/C, Budapest, 1117, Hungary

    Teshome Bayleyegn, István Faragó & Ágnes Havasi

  2. MTA-ELTE Numerical Analysis and Large Networks Research Group, Pázmány Péter s. 1/C, Budapest, 1117, Hungary

    István Faragó & Ágnes Havasi

  3. Institute of Mathematics, Budapest University of Technology and Economics, Egry J. u. 1., Budapest, 1111, Hungary

    István Faragó

Authors
  1. Teshome Bayleyegn
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  2. István Faragó
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  3. Ágnes Havasi
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Corresponding author

Correspondence to István Faragó .

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Editors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Georgiev

  2. Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Maria Datcheva

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir Georgiev

  4. Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    Geno Nikolov

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Bayleyegn, T., Faragó, I., Havasi, Á. (2023). On the Consistency and Convergence of Repeated Richardson Extrapolation. In: Georgiev, I., Datcheva, M., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2022. Lecture Notes in Computer Science, vol 13858. Springer, Cham. https://doi.org/10.1007/978-3-031-32412-3_5

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  • DOI: https://doi.org/10.1007/978-3-031-32412-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-32411-6

  • Online ISBN: 978-3-031-32412-3

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