On the Numerical Solution of Perturbed Bifurcation Problems

Mohamed Elgindi, R. W. Langer

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Some numerical schemes, based upon Newton’s and chord methods, for the computations of the perturbed bifurcation points as well as the solution curves through them, are presented. The “initial” guesses for Newton’s and chord methods are obtained using the local analysis techniques and proved to fall into the neighborhoods of contraction for these methods. In applications the “perturbation” parameter represents a physical quantity and it is desirable to use it to parameterize the solution curves near the perturbed bifurcation point. In this regard, it is shown that, for certain classes of the perturbed bifurcation problems, 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.

Original languageEnglish
Pages (from-to)561-570
Number of pages10
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume18
Issue number3
DOIs
Publication statusPublished - 1995
Externally publishedYes

Fingerprint

Bifurcation Point
Bifurcation
Chord or secant line
Numerical Solution
Parameter Perturbation
Curve
Parameterise
Guess
Numerical Scheme
Contraction

Keywords

  • bifurcation from the trivial solution
  • Newton's and chord methods
  • Perturbed bifurcation
  • singular perturbation

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

On the Numerical Solution of Perturbed Bifurcation Problems. / Elgindi, Mohamed; Langer, R. W.

In: International Journal of Mathematics and Mathematical Sciences, Vol. 18, No. 3, 1995, p. 561-570.

Research output: Contribution to journalArticle

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