On the construction of error estimators for implicit Runge-Kutta methods
type: Item
instance of: scholarly article
title: On the construction of error estimators for implicit Runge-Kutta methods
zbMATH Open document ID: 0897.65051
DOI: 10.1016/S0377-0427(97)00166-0
author: Gustaf Söderlind
author: Jacques J. B. de Swart
published in: Journal of Computational and Applied Mathematics
publication date: 1998-10-25T00:00:00Z
review text: When an implicit Runge-Kutta method is applied to a stiff system of ordinary differential equations it is well known that an estimation of the local error which gives realistic estimates for stiff components is rather difficult. The stiff error components may be highly overestimated if the stability function is unbounded at infinity. There are codes improving such inadequate error estimates by premultiplying the estimate by a filter matrix which damps or removes large stiff error components. The authors resolve this problem by introducing an implicit error estimator with the desired properties for stiff components without employing the somewhat arbitrary technique of filter matrix. The proposed error estimator contains a free parameter determining the magnitude of the error; the authors show how this parameter is to be selected on the basis of the method properties. The construction principles for the error estimator can be adapted to all implicit Runge-Kutta methods. For details the reader is referred to the interesting note.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34E13
zbMATH DE Number: 1115942
zbMATH Keywords: error bounds
zbMATH Keywords: implicit Runge-Kutta method
zbMATH Keywords: stiff system
zbMATH Keywords: stability
reviewed by: Hans Ade
describes a project that uses: RODAS
MaRDI profile type: Publication
cites work: Solving Ordinary Differential Equations I
cites work: Q4714145
cites work: Q4000414
cites work: Error estimators for stiff differential equations
description: scientific article; zbMATH DE number 1115942