P-stable modification of the Numerov method
type: Item
instance of: scholarly article
title: P-stable modification of the Numerov method
zbMATH Open document ID: 0666.65050
DOI: 10.1016/0898-1221(88)90260-X
author: S. H. Smith
publication date: 1988-01-01T00:00:00Z
review text: The fourth order Numerov method applies to approximate the solution to second order periodic initial value problems of the form \(x''=f(t,x),\) \(x(t_ 0)=x_ 0,\) \(x'(t_ 0)=x'_ 0,\) but it is not p-stable. To be p-stable the method must have an infinite interval of periodicity while this method has periodic interval (0,6). As stated in the title of the paper the method is modified so as to be p-stable.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4090706
zbMATH Keywords: P-stability
zbMATH Keywords: fourth order Numerov method
zbMATH Keywords: second order periodic initial value problems
zbMATH Keywords: interval of periodicity
reviewed by: John B. Butler jun.
MaRDI profile type: Publication
cites work: Stabilization of Cowell's method
cites work: Symmetric Multistip Methods for Periodic Initial Value Problems
cites work: High order P-stable formulae for the numerical integration of periodic initial value problems
cites work: A Sixth-order P-stable Symmetric Multistep Method for Periodic Initial-value Problems of Second-order Differential Equations
cites work: High-accuracy P-stable Methods for y″ = f(t, y)
full work available at URL: 0898-1221(88)90260-x
OpenAlex ID: W2086360267
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4090706