A method for finding the periodic solution of autonomous ordinary differential equations

摘要

Using the least square method, the problem of computing periodic solutions of autonomous ordinary differential equations has been reduced to a problem of minimization on a normal plane. The conjugate gradient method is used to yield a successive initial value, and the Runge–Kutta method is used to solve the initial value problem in the ordinary differential equations. So a new method for this problem is formed. To illustrate, it is applied to the Brusselator model and Field-Noyes model of Belousov–Zhabotinskii reactions. The numerical results obtained show that this method is very efficient.