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On a method of characteristics for solving a hyperbolic equation of second order

Über ein Charakteristikenverfahren zur Lösung einer hyperbolischen Differentialgleichung zweiter Ordnung

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Abstract

The hyperbolic initial-boundary value problem for the second order equationa(t,x,u)u tt +2b(t,x,u)u tx +c(t,x,u)u xx =d(t,x,u,u t ,u x ) is solved by a special method of characteristics involving no difference equations foru t andu x . The discrete solution has an asymptotic expansion in even powers of the step size. Therefore, the numerical results can be improved by extrapolation to the limit.

Zusammenfassung

Das Anfangsrandwertproblem für die hyperbolische Differentialgleichunga(t,x,u)u tt +2b(t,x,u)u tx +c(t,x,u)u xx =d(t,x,u,u t ,u x ) zweiter Ordnung wird mit Hilfe eines Charakteristikenverfahrens gelöst, das keine Differenzengleichungen füru t undu x benutzt. Die Lösung des diskretisierten Problems besitzt eine asymptotische Entwicklung nach geraden Potenzen der Schrittweite. Daher können die numerischen Ergebnisse durch Extrapolation verbessert werden.

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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-5000, Köln 41, Federal Republic of Germany

    W. Hackbusch

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  1. W. Hackbusch
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Hackbusch, W. On a method of characteristics for solving a hyperbolic equation of second order. Computing 20, 47–60 (1978). https://doi.org/10.1007/BF02241901

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  • DOI: https://doi.org/10.1007/BF02241901

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