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An algorithm for solving multi-point boundary value problems

Ein Algorithmus zur Lösung von Mehrpunkt-Randwertproblemen

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Abstract

We describe a method for computing solutions of multi-point boundary value problems, where the polychotomic structure of the underlying solution space is specifically exploited. After the system is integrated in a multiple shooting way, the resulting linear system is solved by a special decoupling algorithm that takes into account the fact that the dichotomy on each interval is potentially different (in contrast to the two point case). A number of examples sustains the theory.

Zusammenfassung

Wir beschreiben ein Verfahren zur Berechnung von Lösungen von Mehrpunkt-Randwertproblemen, wobei die Unterteilungsstruktur des Lösungsraumes speziell ausgenützt wird. Nach der Integration des Systems mit Hilfe der Mehrziel-Methode wird das entstandene lineare Gleichungssystem mit einem speziellen Entkopplungs-Algorithmus gelöst, der berücksichtigt, daß die Randbedingungen für jedes Teilintervall verschiedenartig sein können (im Gegensatz zum Zweipunkt-Fall). Die Theorie wird durch einige Beispiele bestätigt.

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Authors and Affiliations

  1. Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4, 2600, Canberra, A.C.T., Australia

    F. R. de Hoog

  2. Faculteit Wiskunde en Informatica, Technische Universiteit Eindhoven, Postbus 513, 5600 MB, Eindhoven, The Netherlands

    R. M. M. Mattheij

Authors
  1. F. R. de Hoog
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  2. R. M. M. Mattheij
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de Hoog, F.R., Mattheij, R.M.M. An algorithm for solving multi-point boundary value problems. Computing 38, 219–234 (1987). https://doi.org/10.1007/BF02240097

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  • DOI: https://doi.org/10.1007/BF02240097

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