A one-step integration routine for normal differential systems, based on Gauss-Legendre quadrature

摘要

We introduce an integration procedure for normal differential systems, implemented in PASCAL, and based on a one-step method using Gauss-Legendre integration.This procedure permits several levels of accuracy and determines an approximate solution of the differential system on an arbitrary user defined partition PN = {t0 = a, t1,…,tN−1, tN=b:ti−1 < ti, i=1,…,N} of [a, b] ⊂R, as well as an error estimation.An interesting application for the method was provided by the study of the nature, the stability and an accurate determination of the bifurcation points of the harmonic and subharmonic solutions of the forced Duffing oscillator, in order to show the onset of chaotic behaviour of the system for certain ranges of its forcing frequency.