On the numerical solution of perturbed bifurcation problems
type: Item
instance of: scholarly article
title: On the numerical solution of perturbed bifurcation problems
zbMATH Open document ID: 0834.65047
DOI: 10.1155/S0161171295000718
author: M. B. M. Elgindi
author: Robert W. Langer
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1996-03-31T00:00:00Z
full work available at URL: https://eudml.org/doc/47372
full work available at URL: issue-3.html
review text: This paper deals with the perturbed bifurcation problem \(G(x, \lambda, \tau) = 0\), where \(G : H \times \mathbb{R} \times \mathbb{R} \to H\) is a smooth mapping, \(H\) is a real Hilbert space, \(\lambda\) is the bifurcation parameter, and \(\tau\) is the perturbation parameter. Some numerical schemes, based upon Newton's and chord methods, for the computation of the perturbated bifurcation points and of the solution curves through them are presented. The techniques go along the same lines as those of \textit{D. W. Decker} and \textit{H. B. Keller} [Commun. Pure Appl. Math. 34, 149-175 (1981; Zbl 0476.34055)] for the bifurcation problem \(G(x, \lambda, 0) = 0\). It is shown that Newton's and chord methods can be used to follow the solution curves in a neighborhood of the perturbed bifurcation point while the perturbation parameter is kept fixed. Numerical examples are given.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 58E07
zbMATH DE Number: 785313
zbMATH Keywords: Newton method
zbMATH Keywords: numerical examples
zbMATH Keywords: perturbed bifurcation problem
zbMATH Keywords: Hilbert space
zbMATH Keywords: chord methods
reviewed by: Viorel Arnăutu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 785313