论文标题
适用于普通微分方程的自适应分段多灵
Adaptive Piecewise Poly-Sinc Methods for Ordinary Differential Equations
论文作者
论文摘要
我们提出了一种基于普通微分方程的SINC点的自适应分段近似方法的新方法。自适应方法是一种分段搭配方法，该方法利用多明文插值达到预设的近似准确性水平。我们的工作扩展了自适应分段多线的方法来函数近似，为此，我们对自适应方法进行了先验误差估计，并显示了其在迭代次数中的指数收敛性。在这项工作中，我们显示了从分段搭配方法获得的先验误差估计的迭代次数中的指数收敛，前提是对存在SINC点处普通微分方程的精确解的良好估计值存在。我们使用统计方法进行细化。自适应贪婪的分段多形算法在常规和僵硬的普通微分方程上进行了验证。
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.
