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.

翻译：我们根据普通差分方程的辛克点提出了一种新的适应性计件近似法方法。 适应性方法是一种小巧合用法,它利用多辛基内插法达到近点的预设精确度。 我们的工作扩展了适应性计件多辛基方法,以功能近似。 为此,我们得出了适应性方法的先验误差估计值,并显示了其迭代数的指数趋同。 在这项工作中,我们显示了从小巧合用法中获得的先验误差估计数的指数趋同,只要对辛克点普通差分方程的精确解法有良好的估计。 我们用统计方法来完善分区。 适应性贪婪多辛基算法则以常规和僵硬的普通差分方程进行验证。