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.
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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Supported in part by the ONERA and by the DRET under grant n0 89.34.401.00.470.75.01
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Chartier, P., Philippe, B. A parallel shooting technique for solving dissipative ODE's. Computing 51, 209–236 (1993). https://doi.org/10.1007/BF02238534
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DOI: https://doi.org/10.1007/BF02238534