New algorithms for the evaluation of complex bifurcation points in ordinary differential equations. A comparative numerical study
type: Item
instance of: scholarly article
title: New algorithms for the evaluation of complex bifurcation points in ordinary differential equations. A comparative numerical study
zbMATH Open document ID: 0566.65069
DOI: 10.1016/0096-3003(84)90005-5
published in: Applied Mathematics and Computation
publication date: 1984-01-01T00:00:00Z
review text: The authors propose two new algorithms for the numerical evaluation of Hopf bifurcation points. In contrast to two earlier published techniques [cf. the second author, SIAM J. Appl. Math. 38, 103-107 (1980; Zbl 0462.65046); Chem. Engrg. Sci. 34, 1078-1080 (1979)] they do not require the computation of the coefficients of the characteristic polynomials. Numerical experiments are performed for two typical examples from chemical reaction engineering consisting of systems of four ordinary differential equations in order to compare the effectiveness of the four algorithms with respect to memory requirements, arithmetical operations and domain and rate of convergence.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 80A32
zbMATH DE Number: 3903895
zbMATH Keywords: multiplicity of solutions
zbMATH Keywords: iterative methods
zbMATH Keywords: Hopf bifurcation points
zbMATH Keywords: Numerical experiments
zbMATH Keywords: chemical reaction engineering
author: Martin Holodniok
author: M. Kubíček
reviewed by: Hansgeorg Jeggle
MaRDI profile type: Publication
full work available at URL: 0096-3003(84)90005-5
OpenAlex ID: W2069913441
cites work: Algorithm for Evaluation of Complex Bifurcation Points in Ordinary Differential Equations
cites work: Q3311595
cites work: Numerical solution of bifurcation problems for ordinary differential equations
cites work: Q1233671
cites work: Q3908398
cites work: Numerical computation of branch points in ordinary differential equations
cites work: Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations
cites work: Numerical solution of Hopf bifurcation problems
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description: scientific article; zbMATH DE number 3903895