Stiff ODE solvers: A review of current and coming attractions
type: Item
instance of: scholarly article
title: Stiff ODE solvers: A review of current and coming attractions
zbMATH Open document ID: 0614.65078
DOI: 10.1016/0021-9991(87)90001-5
author: George D. Byrne
author: A. C. Hindmarsh
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: This article (62 pages) gives a review of methods and software solvers that are currently in use for stiff ordinary differential equations. Further, it presents a set of 10 stiff problems which show the challenges to the software and the capabilities of the solvers. After an introduction into the notion of stiffness and into related problems (stability, method of lines, differential-algebraic systems), Section 2 presents a survey of methods for stiff problems including some comments on their relative merits. Section 3 is a description of available software. It begins with the history of ODE-solvers based on backward differentiation formulas and describes mainly the codes LSODE, EPISODE and related ones. Other codes (Runge-Kutta, blended and composite multistep, extrapolation, second-derivative) are mentioned briefly. An interesting and important part of this review is Section 4, where a set of 10 stiff problems is given. These examples are fairly representative with respect to many features and include problems arising in partial differential equations. It is shown how they can be solved by LSODE and its variants.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3994946
zbMATH Keywords: review article
zbMATH Keywords: numerical examples
zbMATH Keywords: software solvers
zbMATH Keywords: stiff problems
zbMATH Keywords: stability
zbMATH Keywords: method of lines
zbMATH Keywords: differential-algebraic systems
zbMATH Keywords: backward differentiation formulas
zbMATH Keywords: LSODE
zbMATH Keywords: EPISODE
zbMATH Keywords: Runge-Kutta
zbMATH Keywords: multistep
zbMATH Keywords: extrapolation
describes a project that uses: GEARS
describes a project that uses: LSODE
describes a project that uses: IMSL Numerical Libraries
describes a project that uses: nag
describes a project that uses: ODEPACK
describes a project that uses: EPISODE
describes a project that uses: DASSL
describes a project that uses: Larkin
MaRDI profile type: Publication
full work available at URL: 0021-9991(87)90001-5
OpenAlex ID: W2167044111
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