Abstract
The motivation for the present study is derived from the fact that time mangaement is an integral part of good engineering practice. The present study investigated the quantification of the required computation time using two nonlinear and harmonically excited oscillators (Pendulum and Duffing) as case studies. Simulations with personal computer were effected for Runge-Kutta schemes (RK2, RK3, RK4, RK5, RK5M) and one blend (RKB) over thirty five thousand and ten excitation periods consisting the unsteady and steady solutions. The need for validation of the developed FORTRAN90 codes by comparing Poincare results with their conterpart from the literature informed the choice of simulation parameters. However, the simulation time was monitored at three lengths of excitation period (15000, 25000 and 35000) using the current time subroutine call command.
 The validation Poincaré results obtained for all the schemes including RKB compare well with the counterpart available in the literature for both Pendulum and Duffing. The actual computation time increases with increasing order of scheme, but suffered a decrease for the blended scheme. The diffencerence in computation time required between RK5 and RK5M is negligible for all studied cases. The actual computational time for Duffing (5-33seconds) remain consistently higher for corresponding Pendulum (3-23seconds) with difference (2-10seconds). Interestingly, the quantitative difference between the corresponding normalised computation time for systems and schemes is insignificant. It is insensitive to systems and schemes and formed a simple average ratio{ } for RK2, RK3, RK4, RK5, RK5M and RKB respectively. It is concluded that the end justified the means provided that computation accuracy is assured using the higher order scheme (with higher computational time ratio).
Highlights
Computer simulations has been described as a process of designing a model of a real system, implementing the model as a computer program, and performing experiments with the model for the rationale of understanding the behaviour of the system, or evaluating strategies for the operation of the system (Classweb, 2013)
The actual computation time increases non-uniformly from second order Runge-Kutta scheme to Butchers’ (1964) modified fifth order schem and suffered dercrease on blended scheme for both Pendulum and Duffing oscillators.The actual computation time required for the simulation of the dynamics of pendulum is in the range (323seconds) while for the Duffing the range is (5-33seconds)
The pendulum recorded higher actual computation time consistently compared with its Duffing counterpart and for corresponding cases
Summary
Computer simulations has been described as a process of designing a model of a real system , implementing the model as a computer program, and performing experiments with the model for the rationale of understanding the behaviour of the system, or evaluating strategies for the operation of the system (Classweb, 2013). Their research paper is a great contribution to computer time management in simulation of dynamical systems. Ludovic et al (2002) proposed an automatic time stepping algorithm useful for numerical simulations of nonlinear dynamics. The authors learnt from research experience that constant step size strategies generally lead to divergence or extremely costly computations This motivated the authors to initiate an algorithm that automatically takes decision in order to update the tangent matrix or stopping the iterations. The authors demonstrated that this technique has reduced the computational time cost using several real life industrial problems. This is no doubt a great contribution to researchers’ efforts in saving the computer time required for numerical simulations. The overall simulation time can be further reduced by using MATLAB distributed computing server to run the simulations on a computer cluster
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