Abstract
This paper deals withB-convergence analysis of linearly implicit Runge-Kutta methods as applied to stiff, semilinear problems of the formy′(t)=Ty(t)+g(t,y). We analyse the discrepancy between the local and global order reduction. We show that linearly implicit Runge-Kutta methods ofB-consistency orderq have theB-convergence orderq+1 for many singularly perturbed problems with constant stiff part. Numerical examples illustrate the theoretical results.
Zusammenfassung
Die Arbeit befaßt sich mitB-Konvergenzuntersuchungen linear impliziter Runge-Kutta-Verfahren, angewandt auf steife semilineare Differentialgleichungen der Gestalty′(t)=Ty(t)+g(t,y). Es wird die Diskrepanz zwischen lokaler und globaler Ordnungsreduktion analysiert. Wir zeigen, daß linear implizite Runge-Kutta-Methoden derB-Konvergenzordnungq für eine gewisse Klasse singulär gestörter Probleme mit konstant steifem Anteil dieB-Konvergenzordnungq+1 besitzt. Numerische Beispiele bestätigen die theoretischen Resultate.
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Strehmel, K., Weiner, R. & Dannehl, I. A study ofB-convergence of linearly implicit Runge-Kutta methods. Computing 40, 241–253 (1988). https://doi.org/10.1007/BF02251252
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DOI: https://doi.org/10.1007/BF02251252