Numerical solutions for a coupled non-linear oscillator

Abba Gumel, W. F. Langford, E. H. Twizell, J. Wu

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A second-order accurate numerical method has been proposed for the solution of a coupled non-linear oscillator featuring in chemical kinetics. Although implicit by construction, the method enables the solution of the model initial-value problem (IVP) to be computed explicitly. The second-order method is constructed by taking a linear combination of first-order methods. The stability analysis of the system suggests the existence of a Hopf bifurcation, which is confirmed by the numerical method. Both the critical point of the continuous system and the fixed point of the numerical method will be seen to have the same stability properties. The second-order method is more competitive in terms of numerical stability than some well-known standard methods (such as the Runge-Kutta methods of order two and four).

Original languageEnglish (US)
Pages (from-to)325-340
Number of pages16
JournalJournal of Mathematical Chemistry
Volume28
Issue number4
StatePublished - Dec 2000
Externally publishedYes

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Nonlinear Oscillator
Coupled Oscillators
Numerical methods
Numerical Solution
Numerical Methods
Hopf bifurcation
Runge Kutta methods
Initial value problems
Convergence of numerical methods
Reaction kinetics
Chemical Kinetics
Continuous System
Numerical Stability
Runge-Kutta Methods
Hopf Bifurcation
Initial Value Problem
Linear Combination
Stability Analysis
Critical point
Fixed point

Keywords

  • Coupled oscillator
  • Hopf bifurcation
  • Numerical method
  • Stability

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

Gumel, A., Langford, W. F., Twizell, E. H., & Wu, J. (2000). Numerical solutions for a coupled non-linear oscillator. Journal of Mathematical Chemistry, 28(4), 325-340.

Numerical solutions for a coupled non-linear oscillator. / Gumel, Abba; Langford, W. F.; Twizell, E. H.; Wu, J.

In: Journal of Mathematical Chemistry, Vol. 28, No. 4, 12.2000, p. 325-340.

Research output: Contribution to journalArticle

Gumel, A, Langford, WF, Twizell, EH & Wu, J 2000, 'Numerical solutions for a coupled non-linear oscillator', Journal of Mathematical Chemistry, vol. 28, no. 4, pp. 325-340.
Gumel, Abba ; Langford, W. F. ; Twizell, E. H. ; Wu, J. / Numerical solutions for a coupled non-linear oscillator. In: Journal of Mathematical Chemistry. 2000 ; Vol. 28, No. 4. pp. 325-340.
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