Computing

, Volume 43, Issue 4, pp 377–390 | Cite as

1D-grid generation by monotone iteration discretization

  • Mansour Al-Zanaidi
  • Christian Grossmann
Article
  • 70 Downloads

Summary

On the basis of the monotone discretization technique, we propose in this paper a new feedback grid generation principle for weakly nonlinear 2-point boundary value problems. By means of available estimations resulting from lower and upper solutions the grid can be refined automatically. The monotonicity of the method is guaranteed by principles of monotone iterations. The convergence properties of the proposed algorithm are analyzed.

AMS Subject Classifications

65L10 65L50 65L60 

Key words

differential equations boundary value problems enclosures grid generation 

Eindimensionale Gittergenerierung durch monotone Diskretisierungs-Iteration

Zusammenfassung

In der vorliegenden Arbeit wird ein Gittersteuerungsprinzip auf der Basis von monotonen Diskretisierungs-Iterations-Verfahren und der damit erzeugten Lösungseinschließungen bei schwach nichtlinearen 2-Punkt-Randwertaufgaben vorgeschlagen. Mittels verfügbarer Schranken wird das Gitter automatisch erzeugt. Die Monotonie des Verfahrens ist dabei durch Prinzipien der monotonen Iteration gesichert. Es werden die Konvergenzeigenschaften des vorgeschlagenen Verfahrens analysiert.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Mansour Al-Zanaidi
    • 1
  • Christian Grossmann
    • 2
  1. 1.Dept. MathematicsKuwait UniversitySafatKuwait
  2. 2.Dept. MathematicsDresden University of TechnologyDresden

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