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Stability of numerical methods for volterra integro-differential equations

Stabilität numerischer Verfahren zur Lösung Volterrascher Integrodifferentialgleichungen

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Abstract

A theory of weak stability for linear multistep methods for the numerical solution of Volterra integro-differential equations is developed, and a connection between this theory and the corresponding theory for ordinary differential equations is established. In addition, the order of such methods is discussed, and a new starting procedure is proposed and analyzed.

Zusammenfassung

Die Theorie der Schwachen Stabilität linearer Mehrschrittverfahren zur numerischen Lösung von Volterraschen Integrodifferentialgleichungen wird beschrieben, wobei ein enger Zusammenhang mit der entsprechenden Theorie für gewöhnliche Differentialgleichungen aufgezeigt wird. Ferner wird die Ordnung solcher Verfahren untersucht, und eine neue Methode zur Erzeugung der notwendigen Startwerte wird hergeleitet.

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References

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Authors and Affiliations

  1. Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada

    H. Brunner

  2. Department of Mathematics, University of Dundee, Dundee, Scotland

    J. D. Lambert

Authors
  1. H. Brunner
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  2. J. D. Lambert
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Additional information

With 1 Figure

This research was supported by the National Research Council of Canada (Grant No. A-4805).

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Brunner, H., Lambert, J.D. Stability of numerical methods for volterra integro-differential equations. Computing 12, 75–89 (1974). https://doi.org/10.1007/BF02239501

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  • DOI: https://doi.org/10.1007/BF02239501

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