Abstract
Iterated Defect Correction (IDeC) is a technique for improving successively an approximate solution of a given problemFy=0. One of the most important fields of application of this principle are differential equations. Here, IDeC can be used as a technique for increasing the order of a discretization method and thus for improving the accuracy. In this paper a metalgorithm for the class of IDeC-methods for differential equations is presented and analyzed. For every component of this metalgorithm conditions are given which guarantee a certain order of accuracy. These conditions are of particular importance for practical applications, as far as the implementation of IDeC-methods is concerned.
Zusammenfassung
Die Iterierte Defektkorrektur (IDeC) ist ein Verfahren zur schrittweisen Verbesserung einer Näherungslösung eines gegebenen ProblemsFy=0. Eines der wichtigsten Anwendungsgebiete dieses Prinzips sind Differentialgleichungen. Die IDeC kann dort als Methode zur Verbesserung der Ordnung eines Diskretisierungsverfahrens, und damit zur Verbesserung der Genauigkeit eingesetzt werden. In der vorliegenden Arbeit wird ein Metaalgorithmus für die Klasse, der IDeC-Verfahren für Differential-gleichungen vorgestellt und analysiert. Für jeden “Baustein” dieses Metaalgorithmus werden Bedingungen angegeben, die es gewährleisten, daß eine bestimmte Ordnung erreicht wird. Diese Bedingungen sind von großer praktischer Bedeutung, wenn IDeC-Verfahren als Computer-Programme implementiert werden sollen.
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Frank, R., Ueberhuber, C.W. Iterated defect correction for differential equations part I: theoretical results. Computing 20, 207–228 (1978). https://doi.org/10.1007/BF02251946
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DOI: https://doi.org/10.1007/BF02251946