A class of two-step \(P\)-stable methods for the accurate integration of second order periodic initial value problems
type: Item
instance of: scholarly article
title: A class of two-step \(P\)-stable methods for the accurate integration of second order periodic initial value problems
zbMATH Open document ID: 0594.65057
DOI: 10.1016/0377-0427(86)90080-4
author: U. Ananthakrishnaiah
published in: Journal of Computational and Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The author considers a two parameter family of two-step methods for the numerical integration of second order differential equations \(y''=f(t,y)\). The parameters are determined in such a way that the ''phase-lag'' of the method is minimal. This is equivalent to the fact that the local error is minimal for the linear problem \(y''+y=0\). It should be remarked that the proposed method is of order six for linear differential equations with constant coefficients, but it is only of order two for the general nonlinear problem. Numerical results are presented only for the linear test equation.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3956355
zbMATH Keywords: second order periodic initial value problems
zbMATH Keywords: P-stable methods
zbMATH Keywords: minimal local error
zbMATH Keywords: two-step methods
zbMATH Keywords: Numerical results
MaRDI profile type: Publication
full work available at URL: 0377-0427(86)90080-4
OpenAlex ID: W2011511697
cites work: A one-step method for direct integration of structural dynamic equations
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description: scientific article; zbMATH DE number 3956355