Representation of the Poincaré sections via Dormand–Prince8 (5, 3)* algorithm

Abstract

This paper deals with the Dormand-Prince 8(5,3) algorithm to analyze two classical nonlinear systems, namely the parametrically damped pendulum and driven damped oscillator , and represents the Poincaré sections in two different ways. The basin of attraction illustrates the changing of the status for the system according to the choosing of the initial conditions. Many of algorithms like Euler, Runge-Kutta 2&4, Runge-Kutta Fehlberg, Extrapolation, Cash-Karp, Adams-Bashforth-Moulton4, Gear & Implicit Gear, Hamming, Milne and Heun show unstable solutions for our systems. The Dormand-Prince8(5,3) algorithm shows a stable solution for big values of integration step size of the time, in comparison with other algorithms.