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Two-sided approximation to periodic solutions of ordinary differential equations. (English) Zbl 0799.65077
A two-sided approximation to the periodic orbit of an autonomous ordinary differential equation system is presented. It is proved that the implicit and explicit Euler difference methods approximate the periodic solution from inner and outer sides separately, provided the periodic orbit is convex and stable.
A numerical example is given to illustrate the result and to point out that the convex condition is necessary for the difference methods in a one-sided approximation and the numerical orbit no longer possesses a one-sided approximation property, if the periodic orbit is not convex.

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C25 Periodic solutions to ordinary differential equations
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