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Bounds for the solution of hyperbolic problems

Schranken für die Lösung hyperbolischer Probleme

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Abstract

This article describes a newly developed and implemented method for computing guaranteed errorbounds for the solution of hyperbolic initial value problems. The basic concepts—modified fixed point theorems and approximated operators—allow an a posteriori error-estimation automatically. Therefore, no a priori knowledge of Lipschitz constants, monotonicity properties or additional error analysis is necessary.

Zusammenfassung

Es wird ein neu entwickeltes und implementiertes Verfahren zur Berechnung von garantierten Fehlerschranken bei hyperbolischen Anfangswert-problemen beschrieben. Die grundlegenden Konzepte—modifizierte Fixpunktsätze und angenäherte Operatoren—gestatten eine automatische a posteriori Fehlerabschätzung. Deshalb ist keine a priori Kenntnis von Lipschitzkonstanten, Monotonieeigenschaften oder zusätzliche Fehleranalyse erforderlich.

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Authors and Affiliations

  1. Mathematisches Institut II der Universität Karlsruhe (TH), Englerstrasse 2, D-7500, Karlsruhe, Germany

    H. -J. Dobner

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  1. H. -J. Dobner
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Dobner, H.J. Bounds for the solution of hyperbolic problems. Computing 38, 209–218 (1987). https://doi.org/10.1007/BF02240096

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  • DOI: https://doi.org/10.1007/BF02240096

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