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Spline collocation approximation to periodic solutions of ordinary differential equations. (English) Zbl 0776.65051
A spline collocation method is used to approximate the periodic solution of a nonlinear autonomous differential equation. It is shown that the solution of the cubic spline approximation problem has the error bound $$O(h^ 4)$$. As an example, the periodic solution of the van der Pol equation is computed by this method.
Reviewer: L.I.Grimm (Rolla)

##### MSC:
 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L07 Numerical investigation of stability of solutions to ordinary differential equations 65L70 Error bounds for numerical methods for ordinary differential equations 34A30 Linear ordinary differential equations and systems 34C25 Periodic solutions to ordinary differential equations