Abstract
There is a large gap between the theoretical results about iterated defect corrections (IDeC) and practical implementations of IDeC methods for stiff systems. This paper tries to close this gap by providing general principles which are essential for the construction of efficient IDeC codes. Numerical results gathered with one particular IDeC based experimental code furnish evidence of the inherent power of the defect correction concept in the context of stiff systems of ordinary differential equations.
Zusammenfassung
Zwischen den theoretischen Resultaten über die iterierte Defektkorrektur (IDeC) und praktischen Implementierungen von IDeC-Verfahren für steife Differentialgleichungen klafft eine beträchtliche Lücke. Die vorliegende Arbeit versucht diese Lücke zu schließen, indem allgemeine Konstruktionsprinzipien für IDeC-Programme angegeben werden. Die im IDeC-Prinzip potentiell vorhandenen Möglichkeiten kommen in numerischen Resultaten zum Ausdruck, die mit einem Experimentierprogramm zur Lösung steifer Differentialgleichungen gewonnen wurden.
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Ueberhuber, C.W. Implementation of defect correction methods for stiff differential equations. Computing 23, 205–232 (1979). https://doi.org/10.1007/BF02252129
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DOI: https://doi.org/10.1007/BF02252129