  We propose a new method of adaptive piecewise approximation based on Sinc
points for ordinary differential equations. The adaptive method is a piecewise
collocation method which utilizes Poly-Sinc interpolation to reach a preset
level of accuracy for the approximation. Our work extends the adaptive
piecewise Poly-Sinc method to function approximation, for which we derived an a
priori error estimate for our adaptive method and showed its exponential
convergence in the number of iterations. In this work, we show the exponential
convergence in the number of iterations of the a priori error estimate obtained
from the piecewise collocation method, provided that a good estimate of the
exact solution of the ordinary differential equation at the Sinc points exists.
We use a statistical approach for partition refinement. The adaptive greedy
piecewise Poly-Sinc algorithm is validated on regular and stiff ordinary
differential equations.
