Lokale Fehlerschätzung mittels modifizierter Richardson-Extrapolation in linear impliziten Einschrittverfahren
We describe a modified Richardson extrapolation for error estimate in a Rosenbrock-Wanner procedure and in an adaptive Runge-Kutta procedure. This method requires only very little extra computation to calculate the solution with step-length 2h. The basic idea of this method is described by \textit{T. D. Bui} and \textit{S. W. H. Poon} [BIT 21, 168-174 (1981; Zbl 0456.65045)]. However the method of Bui and Poon is only correct for linear differential equations. The aim of our paper is to present a correct version for nonlinear stiff systems. Examples of strong A-stable ROW- and ARK-procedures with modified Richardson extrapolation are presented.
scientific article; zbMATH DE number 3870508