Accuracy and Reliability of Piecewise Constant Method in Studying the Responses of Nonlinear Dynamic Systems

Abstract

Accuracy and reliability of the numerical simulations for nonlinear dynamical systems are investigated with fourthorder Runge–Kutta method and a newly developed piecewiseconstant (PT) method. Nonlinear dynamic systems with external excitations are studied and compared with the two numerical approaches. Semianalytical solutions for the dynamic systems are developed by the PT approach. With employment of a periodicityratio (PR) method, the regions of regular and irregular motions are determined and graphically presented corresponding to the system parameters, for the comparison of accuracy and reliability of the numerical methods considered. Central processing unit (CPU) time executed in the numerical calculations with the two numerical methods are quantitatively investigated and compared under the same computational conditions. Due to its inherent drawbacks, as found in the research, Runge–Kutta method may cause information missing and lead to incorrect conclusions in comparing with the PT method.