Linearly-implicit Runge-Kutta methods based on implicit Runge-Kutta methods
type: Item
instance of: scholarly article
title: Linearly-implicit Runge-Kutta methods based on implicit Runge-Kutta methods
zbMATH Open document ID: 0790.65059
DOI: 10.1016/0168-9274(93)90129-F
author: Jürgen Bruder
published in: Applied Numerical Mathematics
publication date: 1994-06-23T00:00:00Z
review text: Linearly-implicit Runge-Kutta methods (LIRKM), based on explicit Runge- Kutta schemes, are compared with implicit Runge-Kutta methods (IRKM) which require the solution of nonlinear equations by Newton-like methods. In particular, the consistency of LIRKM is investigated and the numerical expense of IRKM and LIRKM is considered. It is shown that the implementation of IRKM as a LIRKM preserves the order of IRKM and gives iterations which are near to the Newton iterations.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 459311
zbMATH Keywords: linearly-implicit Runge-Kutta methods
zbMATH Keywords: Newton-like methods
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
cites work: Q3740148
cites work: Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems
cites work: On the Butcher group and general multi-value methods
cites work: Q4000061
cites work: Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden
description: scientific article; zbMATH DE number 459311