\(A\)-stable parallel block methods for ordinary and integro-differential equations
type: Item
instance of: scholarly article
title: \(A\)-stable parallel block methods for ordinary and integro-differential equations
zbMATH Open document ID: 0749.65050
DOI: 10.1016/0168-9274(92)90021-5
author: B. P. Sommeijer
author: W. Couzy
author: P. J. van der Houwen
published in: Applied Numerical Mathematics
publication date: 1992-09-26T00:00:00Z
review text: For the numerical integration of stiff equations \(y'=f(y)\) the authors propose the use of block methods \(Y_{n+1}=AY_ n+hBf(Y_ n)+hDf(Y_{n+1})\) where \(A\), \(B\) and \(D\) are \(k\times k\) matrices. If \(D\) is diagonal and if \(k\) processors are available, then these methods require an amount of work which is similar to what a linear multistep method requires when implemented on a uni-processor machine. However, better stability properties can be achieved. New \(A\)-stable methods of orders 3 and 4 and \(A(\alpha)\)-stable methods \((\alpha > 89.9^ 0)\) of order 5 are presented. The use of these block methods for Volterra integro-differential equations is discussed and some numerical experiments are reported.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 54680
zbMATH Keywords: parallel computation
zbMATH Keywords: block implicit methods
zbMATH Keywords: \(A\)-stability
zbMATH Keywords: \(A\)-stable methods
zbMATH Keywords: stiff equations
zbMATH Keywords: linear multistep method
zbMATH Keywords: stability
zbMATH Keywords: Volterra integro- differential equations
zbMATH Keywords: numerical experiments
reviewed by: Ernst Hairer
MaRDI profile type: Publication
full work available at URL: 0168-9274(92)90021-5
OpenAlex ID: W2036941611
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description: scientific article; zbMATH DE number 54680