Numerical solutions for a coupled non-linear oscillator

A. B. Gumel, W. F. Langford, E. H. Twizell, J. Wu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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
Issue number4
StatePublished - Dec 2000
Externally publishedYes


  • Coupled oscillator
  • Hopf bifurcation
  • Numerical method
  • Stability

ASJC Scopus subject areas

  • General Chemistry
  • Applied Mathematics


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