Investigation of Excited Duffing’s Oscillator Using Versions of Second Order Runge-Kutta Methods

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Author(s) Salau T. A.O. | Ajide O.O.
Pages 679-687
Volume 1
Issue 12
Date December, 2012
Keywords Excited Duffing Oscillator, Second order Runge-Kutta, Taylor Series and Poincare Section
Abstract

This investigation derived its strong motivation in the adoption of versions of second-order Runge-Kutta methods where there is presently dearth of relevant literature to re-establish the complicated nature of solution of Duffing oscillator dynamics. The choice of second-order Runge-Kutta methods hinged on its simplest algebraic formulation of relevant coefficients based on Taylor series expansion comparing with its higher order counterpart. Validation of FORTRAN-90 codes of algorithms was achieved by phase plots comparison reference to Dowell (1988) as standard. The nature of simulated solutions were visually determined with scatter plot of phase variables obtained from simultaneous implementation of large number of versions of second-order Runge-Kutta methods in conjunction with the corresponding literature results. Validation results are acceptable to within the accuracy limit of Runge-Kutta methods adopted. The scatter plots on phase plane for cases investigated are well structured and bounded (strange) and compare correspondingly well with literature Poincare sections. This investigation re-establishes the complex nature of solution of Duffings oscillator dynamics. Its established procedures provide an alternative Poincare section method and can be utilised for preliminary verification of system dynamics behaviour subject to confirmation by additional dynamics tests.

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