2-SIDED APPROXIMATION TO PERIODIC-SOLUTIONS OF ORDINARY DIFFERENTIAL-EQUATIONS

A two-sided approximation to the periodic orbit of an autonomous ordinary differential equation system is considered. First some results about variational equation systems for periodic solutions are obtained in Sect. 2. Then it is proved that if the periodic orbit is convex and stable, the explicit difference solution approximates the periodic orbit from the outer part and the implicit one from the inner part respectively. Finally a numerical example is given to illustrate our result and to point out that the numerical solution no longer has a one-sided approximation property, if the periodic orbit is not convex.