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We propose a new method of adaptive piecewise approximation based on Sincpoints for ordinary differential equations. The adaptive method is a piecewisecollocation method which utilizes Poly-Sinc interpolation to reach a presetlevel of accuracy for the approximation. Our work extends the adaptivepiecewise Poly-Sinc method to function approximation, for which we derived an apriori error estimate for our adaptive method and showed its exponentialconvergence in the number of iterations. In this work, we show the exponentialconvergence in the number of iterations of the a priori error estimate obtainedfrom the piecewise collocation method, provided that a good estimate of theexact solution of the ordinary differential equation at the Sinc points exists.We use a statistical approach for partition refinement. The adaptive greedypiecewise Poly-Sinc algorithm is validated on regular and stiff ordinarydifferential equations.

Adaptive Piecewise Poly-Sinc Methods for Ordinary Differential Equations