Abstract
In the following we give an analysis of the local superconvergence properties of piecewise polynomial collocation methods and related continuous Runge-Kutta-type methods for Volterra integral equations with constant delay. We show in particular that (in contrast to delay differential equations) collocation at the Gauss points does not lead to higher-order convergence and thusm-stage Gauss-Runge-Kutta methods for delay Volterra equations do not possess the orderp=2m.
Zusammenfassung
Diese Arbeit befaßt sich mit Fragen der (lokalen) Superkonvergenz bei Kollokationsverfahren und stetigen impliziten Runge-Kutta-Methoden für Volterrasche Integralgleichungen mit retardiertem Argument. Es wird insbesondere gezeigt, daß (im Gegensatz zu retardierten Differentialgleichungen) Kollokation an den Gauss-Punkten nicht zu einer höheren Konvergenzordnung führt and daß deshalbm-stufige Gauss-Runge-Kutta-Methoden nicht die Ordnungp=2m besitzen.
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Baddour, N., Brunner, H. Continuous Volterra-Runge-Kutta methods for integral equations with pure delay. Computing 50, 213–227 (1993). https://doi.org/10.1007/BF02243812
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DOI: https://doi.org/10.1007/BF02243812