Abstract
The convergence of ROW methods is studied when these methods are applied to the stiff model equation of Prothero and Robinson. It turns out that there are barriers of the attainable order of convergence. Furthermore, the existence of ROW methods is shown the accuracy of which increases asymptotically with the stiffness of the model. The theoretical results are demonstrated by numerical examples.
Zusammenfassung
Es werden die Konvergenzeigenschaften der ROW-Verfahren bei ihrer Anwendung auf das steife Differentialgleichungsmodell von Prothero und Robinson untersucht. Dabei zeigt es sich, daß es Barrieren für die tatsächlich erreichbare Konvergenzordnung gibt. Ferner existieren ROW-Verfahren, deren Genauigkeit asymptotisch mit der Steifheit des Modells zunimmt. Die theoretischen Ergebnisse werden an numerischen Beispielen demonstriert.
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Scholz, S. Order barriers for the B-convergence of ROW methods. Computing 41, 219–235 (1989). https://doi.org/10.1007/BF02259094
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DOI: https://doi.org/10.1007/BF02259094