Simulation of Oscillators Dynamics using Selected Versions of Fourth Order Runge-Kutta Scheme

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Author(s) Salau T. A.O. | Olaiya K.A. | Ajide O.O.
Pages 444-454
Volume 4
Issue 8
Date August, 2014
Keywords RK4 Versions, Oscillator Dynamics, Chaotic, Simulation time step and Poincare Section

Abstract

This study investigated the simulation performance from zero initial conditions across the transient and steady states of six different versions of fourth order Runge-Kutta schemes (RK41, RK42, RK43, RK44, RK45 & RK46-stable and unstable) on cases of linear and nonlinear dynamics. Validation cases were obtained from [1-3] including the periodically and chaotically responding nonlinear excited pendulum at drive frequency of . The simulated results of linear dynamics correlate quantitatively well for all the schemes when compared with the results reported by [1] except for RK44 which was reported less stable by [3]. However for a reduced simulation time step of 0.0025 the simulated results by RK44 improved drastically towards the exact results as well as the results prescribed by other schemes. The schemes performance replicate for the case of periodically behaving nonlinear pendulum. However the simulated results of the chaotic counterpart of the nonlinear pendulum lacked correlation, but all the schemes produced qualitatively the same Poincare section that is qualitatively the same as reported by [2]. Provided the scheme stability is guaranteed, the study results can be adopted in the characterization of dynamic systems.

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