A numerical study of spontaneous bifurcation
type: Item
instance of: scholarly article
title: A numerical study of spontaneous bifurcation
zbMATH Open document ID: 0641.65063
DOI: 10.1016/0377-0427(87)90188-9
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author considers the following problem \((1)\quad u''+f(u)=0,| x| <L\), \(u(\pm L)=0\), where \(f(u)=-u(u-a)(u-b)\), with \(0<a<b\). This problem, which has been of recent interest, is studied numerically. It is shown that a two-sheeted surface of bifurcating solutions in the parameter space \(\{(a,L,u_ 1):\) \(0<a<b\), \(L>0\), \(u_ 1\in {\mathbb{R}}\}\), can be determined numerically, thus giving a complete numerical description of the solution set of (1) and its bifurcations. Discussion on continuation algorithms and numerical results conclude the paper.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 4045049
zbMATH Keywords: two-sheeted surface of bifurcating solutions
zbMATH Keywords: bifurcations
zbMATH Keywords: continuation algorithms
zbMATH Keywords: numerical results
author: Michael W. Smiley
MaRDI profile type: Publication
full work available at URL: 0377-0427(87)90188-9
OpenAlex ID: W2094163008
cites work: Q4112515
cites work: Q4155374
cites work: Q3948194
cites work: Q3886065
cites work: Q3905599
cites work: Bifurcation studies in reaction-diffusion
cites work: Bifurcation studies in reaction-diffusion. II
cites work: On the Existence of Positive Solutions of Semilinear Elliptic Equations
cites work: Q4134254
cites work: Low-dimensional qualitative and numerical approximation of bifurcation in a semilinear elliptic problem
cites work: Eigenfunction methods and nonlinear hyperbolic boundary value problems at resonance
cites work: Q4746129
cites work: Global bifurcation of steady-state solutions
description: scientific article; zbMATH DE number 4045049