论文标题
关于Clenshaw-Curtis搭配的稳定性和准确性
On the Stability and Accuracy of Clenshaw-Curtis Collocation
论文作者
论文摘要
我们研究Clenshaw-Curtis搭配的A稳定性和准确性特征。我们提出了封闭形式的表达式，以评估这些方法的runge-kutta系数。从A稳定性研究中，Clenshaw-Curtis方法是稳定的，最多可达大量节点。高精度是这些方法的另一个好处。数值实验表明，它们可以匹配高斯 - legendre搭配的准确性，高斯 - legendre搭配的精度具有所有runge-kutta方法的最佳精度顺序。
We study the A-stability and accuracy characteristics of Clenshaw-Curtis collocation. We present closed-form expressions to evaluate the Runge-Kutta coefficients of these methods. From the A-stability study, Clenshaw-Curtis methods are A-stable up to a high number of nodes. High accuracy is another benefit of these methods; numerical experiments demonstrate that they can match the accuracy of the Gauss-Legendre collocation, which has the optimal accuracy order of all Runge-Kutta methods.
