Lokale Fehlerschätzung mittels modifizierter Richardson-Extrapolation in linear impliziten Einschrittverfahren
type: Item
instance of: scholarly article
title: Lokale Fehlerschätzung mittels modifizierter Richardson-Extrapolation in linear impliziten Einschrittverfahren
zbMATH Open document ID: 0546.65044
DOI: 10.1007/BF02240184
published in: Computing
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 3870508
zbMATH Keywords: linear implicit methods
zbMATH Keywords: Richardson extrapolation
zbMATH Keywords: error estimate
zbMATH Keywords: Rosenbrock-Wanner
zbMATH Keywords: adaptive Runge-Kutta
zbMATH Keywords: nonlinear stiff systems
zbMATH Keywords: A- stable ROW- and ARK
author: K. Strehmel
author: R. Weiner
MaRDI profile type: Publication
cites work: On the computational aspects for Rosenbrock procedures with built-in error estimates for stiff systems
cites work: Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations
cites work: A study of Rosenbrock-type methods of high order
cites work: Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
cites work: Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden
description: scientific article; zbMATH DE number 3870508