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Guaranteed Error Bounds for a Class of Picard-Lindelöf Iteration Methods

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Book cover Numerical Methods for Differential Equations, Optimization, and Technological Problems

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 27))

Abstract

We present a new version of the Picard-Lindelöf method for ordinary differential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations.

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References

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Authors and Affiliations

  1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), 40014, Jyväskylä, Finland

    Svetlana Matculevich, Pekka Neittaanmäki & Sergey Repin

  2. V.A. Steklov Institute of Mathematics in St. Petersburg, Fontanka 27, 191024, St. Petersburg, Russia

    Sergey Repin

Authors
  1. Svetlana Matculevich
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  2. Pekka Neittaanmäki
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  3. Sergey Repin
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Corresponding author

Correspondence to Svetlana Matculevich .

Editor information

Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Sergey Repin

  2. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Timo Tiihonen

  3. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Tero Tuovinen

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Matculevich, S., Neittaanmäki, P., Repin, S. (2013). Guaranteed Error Bounds for a Class of Picard-Lindelöf Iteration Methods. In: Repin, S., Tiihonen, T., Tuovinen, T. (eds) Numerical Methods for Differential Equations, Optimization, and Technological Problems. Computational Methods in Applied Sciences, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5288-7_10

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  • DOI: https://doi.org/10.1007/978-94-007-5288-7_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5287-0

  • Online ISBN: 978-94-007-5288-7

  • eBook Packages: EngineeringEngineering (R0)

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