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.
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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Al-Zanaidi, M., Grossmann, C. 1D-grid generation by monotone iteration discretization. Computing 43, 377–390 (1990). https://doi.org/10.1007/BF02241656
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DOI: https://doi.org/10.1007/BF02241656