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Numerical solution of the singular Ginzburg-Landau equations by multiple shooting

Numerische Lösung der singulären Ginzburg-Landau-Gleichungen mit Hilfe der Mehrzielmethode

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Abstract

A useful method for the numerical solution of singular two-point boundary value problems by multiple shooting techniques is treated. In a small interval Taylor series expansions are used in orderto kill the numerical singularity. The reliability of the method is demonstrated by solving the Ginzburg-Landau equations arising in the theory of superconductivity.

Zusammenfassung

Es wird eine handliche Methode zur Lösung singulärer Randwertprobleme gewöhnlicher Differentialgleichungen behandelt. Taylorreihenentwicklungen des Systems in einem kleinen Intervall blenden die Singularität aus, so daß die Aufgabe mit der Mehrzielmethode gelöst werden kann. Die Zuverlässigkeit dieses Verfahrens wird bei der Lösung der Ginzburg-Landau-Gleichungen der Supraleitung nachgewiesen.

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Authors and Affiliations

  1. Mathematisches Institut, Technische Universität München, Arcisstraße 21, Postfach 202420, D-8000, München 2, Federal Republic of Germany

    P. Rentrop

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  1. P. Rentrop
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Rentrop, P. Numerical solution of the singular Ginzburg-Landau equations by multiple shooting. Computing 16, 61–67 (1976). https://doi.org/10.1007/BF02241980

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  • DOI: https://doi.org/10.1007/BF02241980

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