A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
type: Item
instance of: scholarly article
title: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
zbMATH Open document ID: 0598.65054
DOI: 10.1016/0377-0427(86)90224-4
author: B. George
published in: Journal of Computational and Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: From authors' summary: In part I [ibid. 11, 277-281 (1984; Zbl 0565.65041)] the authors gave a Noumerov-type method with minimal phase- lag for the integration of second order initial-value problems: \(y''=f(t,y)\), \(y(t_ 0)=y_ 0\), \(y'(t_ 0)=y_ 0'\). However, the method given there is implicit. We show here the interesting result that if the Noumerov-type methods of the paper mentioned above are made explicit with the help of the classical second order method, then there exists a selection of the free parameter for which the resulting method has a considerably small frequency distortion of size \((1/40320)H^ 6\) and also a (slightly) larger interval of periodicity of size 2.75 than the phase-lag of size \((1/12096)H^ 6\) and interval of periodicity of size 2.71 for the implicit method of the authors. More interestingly, it turns out that Noumerov made explicit of the first author [BIT 24, 117- 118 (1984; Zbl 0568.65042)] also has less frequency distortion than the (implicit) Noumerov method.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3965356
zbMATH Keywords: Noumerov-type explicit method
zbMATH Keywords: minimal phase-lag
zbMATH Keywords: second order initial- value problems
zbMATH Keywords: interval of periodicity
reviewed by: Zdzislaw Jackiewicz
MaRDI profile type: Publication
full work available at URL: 0377-0427(86)90224-4
OpenAlex ID: W2060641206
cites work: A one-step method for direct integration of structural dynamic equations
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
cites work: Numerov made explicit has better stability
cites work: Families of fifth order Nyström methods for y''=f(x,y) and intervals of periodicity
description: scientific article; zbMATH DE number 3965356