On error behaviour of partitioned linearly implicit Runge-Kutta methods for stiff and differential algebraic systems
type: Item
instance of: scholarly article
title: On error behaviour of partitioned linearly implicit Runge-Kutta methods for stiff and differential algebraic systems
zbMATH Open document ID: 0702.65073
DOI: 10.1007/BF02017354
author: I. Dannehl
author: K. Strehmel
author: R. Weiner
published in: BIT
publication date: 1990-01-01T00:00:00Z
review text: This paper is concerned with the construction of partitioned linearly implicit Runge-Kutta methods for stiff singularly perturbed problems as well as differential algebraic systems of index 1. The partitioned methods consist of an explicit Runge-Kutta method for the non-stiff subsystem and a linearly implicit method for the stiff subsystem. Order conditions are derived which allow the construction of methods with arbitrary global order. Some numerical examples illustrate these theoretical results.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4151759
zbMATH Keywords: partitioned linearly implicit Runge-Kutta methods
zbMATH Keywords: stiff singularly perturbed problems
zbMATH Keywords: differential algebraic systems of index 1
zbMATH Keywords: Order conditions
zbMATH Keywords: global order
zbMATH Keywords: numerical examples
reviewed by: Kevin Burrage
MaRDI profile type: Publication
cites work: One-step and extrapolation methods for differential-algebraic systems
cites work: On the stability of semi-implicit methods for ordinary differential equations
cites work: Q3831975
cites work: Error of Rosenbrock methods for stiff problems studied via differential algebraic equations
cites work: Q3779682
cites work: Q3827564
cites work: Rosenbrock methods for differential algebraic equations
cites work: Partitioned adaptive Runge-Kutta methods and their stability
cites work: B-convergence results for linearly implicit one step methods
full work available at URL: https://doi.org/10.1007/bf02017354
OpenAlex ID: W1992187514
description: scientific article; zbMATH DE number 4151759