Elements of a general theory of composite integration methods
type: Item
instance of: scholarly article
title: Elements of a general theory of composite integration methods
zbMATH Open document ID: 0682.65042
DOI: 10.1016/0096-3003(89)90108-2
author: Peter Albrecht
published in: Applied Mathematics and Computation
publication date: 1989-01-01T00:00:00Z
review text: The author reviews his own work on a theory of general linear methods for the numerical integration of ordinary differential equations. The first part deals with the concept of stability and the relation between the order of convergence and the local discretization errors. Various results appear as easy consequences of the theory. The second part treats Runge- Kutta methods within this general framework. The approach gives a recursive scheme for determining the order conditions. The format differs from that obtained using elementary differentials and is of interest. This theory of general linear methods offers a valuable alternative to that developed by \textit{J. C. Butcher} [The numerical analysis of ordinary differential equations, Runge-Kutta and general linear methods (1987; Zbl 0616.65072)].
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4117767
zbMATH Keywords: stability
zbMATH Keywords: order of convergence
zbMATH Keywords: local discretization errors
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: order conditions
zbMATH Keywords: general linear methods
MaRDI profile type: Publication
full work available at URL: 0096-3003(89)90108-2
OpenAlex ID: W4244756042
cites work: Q3853064
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description: scientific article; zbMATH DE number 4117767