A METHOD FOR FINDING THE PERIODIC-SOLUTION OF AUTONOMOUS ORDINARY DIFFERENTIAL-EQUATIONS

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.