Investigation of Selected Versions of Fourth Order Runge-Kutta Algorithms as Simulation Tools for Harmonically Excited Nonlinear Pendulum

Abstract

This study employed fifty-five selected versions of the Runge-Kutta (RK) fourth order schemes tagged (RKV_1, RKV_2, …, RKV_55), inclusive is the classical fourth order scheme RKV_55 to simulate the dynamics of harmonically excited nonlinear pendulum using adaptive time step technique over a range of drive parameters, initial conditions and excitation frequencies. A FORTRAN program was developed to carry out the simulation and validated by comparing Poincare section obtained with literature standard. The Poincare sections generated compares favourably with those published in literature, thus validate the algorithm. Furthermore, the study results show that number of steps each Runge-Kutta version used to complete the specified simulation periods of the nonlinear pendulum differs significantly. Ranking the versions by the number of steps indicated that RKV_55 is not the fastest version as other versions such as RKV_2, RKV_8, RKV_9, RKV_10, and RKV_51 outperformed it. In addition, the performance of these versions are not significantly affected by the change in initial condition but are greatly affected by the change in angular drive frequency.