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, Volume 51, Issue 3–4, pp 209–236 | Cite as

A parallel shooting technique for solving dissipative ODE's

  • P. Chartier
  • B. Philippe
Article

Abstract

In this paper, we study different modifications of a class of parallel algorithms, initially designed by A. Bellen and M. Zennaro for difference equations and called “across the steps” methods by their authors, for the purpose of solving initial value problems in ordinary differential equations (ODE's) on a massively parallel computer. Restriction to dissipative problems is discussed which allow these problems to be solved efficiently, as shown by the simulations.

AMS Subject Classification

65L05 65W05 65Q05 

Key words

Massively parallel “across the steps” methods ordinary differential equations dissipative problems 

Eine parallele “shooting” Technik zur Lösung dissipativer gewöhnlicher Differentialgleichungen

Zusammenfassung

In diesem Artikel studieren wir verschiedene Versionen einer Klasse paralleler Algorithmen, die ursprünglich von A. Bellen und M. Zennaro für Differenzengleichungen konzipiert und von ihnen “across the steps” Methode genannt worden ist. Die Autoren verfolgten den Zweck, Anfangswertprobleme bei gewöhnlichen Differentialgleichungen anhand eines massiv parallelen Rechner zu lösen. Wir behandeln die Anwendung auf dissipative Systeme und erreichen eine effiziente Lösung dieser Probleme. Dies wird in einigen Simulationen illustriert.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • P. Chartier
    • 1
  • B. Philippe
    • 2
  1. 1.SIMULOGSt Quentin Yvelines CedexFrance
  2. 2.IRISA/INRIARennes CedexFrance

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