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Monotone iteration discretization algorithm for BVP's

Monotone Iteration bei Diskretisierungen von Randwertproblemen

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Abstract

In this paper we propose a new discretization technique generating enclosures of the solution of a weakly nonlinear 2-point boundary value problem. By means of available extimations lower and upper solutions are generated. The monotonicity of the method is guaranteed by principles of monotone iterations. The convergence properties of the proposed algorithm are analyzed.

Zusammenfassung

In der vorliegenden Arbeit wird eine neue Diskretisierungstechnik zur Erzeugung von Lösungseinschließungen bei schwach nichtlinearen 2-Punkt-Randwertaufgaben vorgeschlagen. Mittels verfügbarer Abschätzungen werden Unter-und Oberlösungen erzeugt. Die Monotonie des Verfahrens wird durch Prinzipien der monotonen Iteration gesichert. Es werden die Konvergenzeigenschaften des vorgeschlagenen Verfahrens analysiert.

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Authors and Affiliations

  1. Dept. Mathematics, Kuwait University, P. O. Box 5969, Safat, Kuwait

    M. Al-Zanaidi

  2. Dept. Mathematics, Dresden University of Technology, Mommsenstrasse 13, DDR-8027, Dresden, German Democratic Republic

    Ch. Grossmann

Authors
  1. M. Al-Zanaidi
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  2. Ch. Grossmann
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Al-Zanaidi, M., Grossmann, C. Monotone iteration discretization algorithm for BVP's. Computing 41, 59–74 (1989). https://doi.org/10.1007/BF02238729

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  • DOI: https://doi.org/10.1007/BF02238729

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