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Defect Correction Algorithms for Stiff Ordinary Differential Equations

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Defect Correction Methods

Part of the book series: Computing Supplementum ((COMPUTING,volume 5))

Abstract

The application of suitable defect correction algorithms to stiff differential equations is analyzed. The B-convergence properties of such algorithms are discussed.

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References

  1. Böhmer, K.: Discrete Newton methods and iterated defect correction. Numer. Math. 37, 167–192 (1981).

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  4. Frank, R., Schneid, J., Ueberhuber, C. W.: Order results for implicit Runge-Kutta-methods applied to stiff systems. SIAM J. Numer. Anal. (to appear).

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  7. Frank, R., Ueberhuber, C. W.: Iterated defect correction for Runge-Kutta-methods. Report Nr. 14/75, Institute for Numerical Mathematics, Technical University of Vienna, 1975.

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  8. Stetter, H. J.: Analysis of Discretization Methods for Ordinary Differential Equations. Berlin-Heidelberg-New York: Springer 1973.

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  9. Zadunaisky, P. E.: A method for the estimation of errors propagated in the numerical solution of a system of ordinary differential equations. In: The Theory of Orbits in the Solar System and in Stellar Systems. Proc. of Intern. Astronomical Union, Symp. 25, Thessaloniki (Contopoulos, G., ed.). 1964.

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Author information

Authors and Affiliations

  1. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 6 - 10, Wien, A-1040, Austria

    Doz. Dr. R. Frank, Prof. Dr. J. Hertling & Dr. H. Lehner

Authors
  1. Doz. Dr. R. Frank
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  2. Prof. Dr. J. Hertling
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  3. Dr. H. Lehner
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, Universität Marburg, Federal Republic of Germany

    Klaus Böhmer

  2. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Austria

    Hans J. Stetter

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© 1984 Springer-Verlag

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Frank, R., Hertling, J., Lehner, H. (1984). Defect Correction Algorithms for Stiff Ordinary Differential Equations. In: Böhmer, K., Stetter, H.J. (eds) Defect Correction Methods. Computing Supplementum, vol 5. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7023-6_2

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  • DOI: https://doi.org/10.1007/978-3-7091-7023-6_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81832-9

  • Online ISBN: 978-3-7091-7023-6

  • eBook Packages: Springer Book Archive

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