On the Stability and Accuracy of Clenshaw-Curtis Collocation
Numerical Analysis
2022-11-29 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2211.14530,
title = {On the Stability and Accuracy of Clenshaw-Curtis Collocation},
author = {Ahmed Atallah and Ahmad Bani Younes},
journal= {arXiv preprint arXiv:2211.14530},
year = {2022}
}