A multi-purpose system for the numerical integration of ODE's
type: Item
instance of: scholarly article
title: A multi-purpose system for the numerical integration of ODE's
zbMATH Open document ID: 0678.65047
DOI: 10.1016/0096-3003(89)90127-6
author: Gustaf Söderlind
published in: Applied Mathematics and Computation
publication date: 1989-01-01T00:00:00Z
review text: The development of a multipurpose integration system is described. The intention is to allow the use of different classes of methods for solving ordinary differential equations, singular perturbation problems as well as implicit differential-algebraic equations. The environment provided is intended to facilitate the testing of new ideas and the comparison of different strategies associated with the implementation of such methods. To illustrate the system the implementation of a new family of methods for non-stiff problems, obtained by adding a difference correction to the backward differential formula (BDF) methods, is outlined. The methods have larger stability regions but bigger error constants than the Adams methods. They facilitate the implementation of a type-intensitive code since it is relatively easy to switch between these and the BDF methods. Detecting stiffness and switching criteria are considered. Compound discretizations, for a partitioned form of the problem are also considered in the context of these methods and a stability analysis based on contractivity is discussed.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4111924
zbMATH Keywords: backward differentiation formula methods
zbMATH Keywords: multipurpose integration system
zbMATH Keywords: singular perturbation
zbMATH Keywords: implicit differential-algebraic equations
zbMATH Keywords: comparison of different strategies
zbMATH Keywords: implementation
zbMATH Keywords: non-stiff problems
zbMATH Keywords: difference correction
zbMATH Keywords: stability regions
zbMATH Keywords: Adams methods
zbMATH Keywords: type-intensitive code
zbMATH Keywords: BDF methods
MaRDI profile type: Publication
full work available at URL: 0096-3003(89)90127-6
OpenAlex ID: W4253458151
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description: scientific article; zbMATH DE number 4111924