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arXiv · 2211.14530

On the Stability and Accuracy of Clenshaw-Curtis Collocation

Ahmed Atallah·Ahmad Bani Younes
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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.

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Ahmed Atallah, Ahmad Bani Younes. 2022-11-26. On the Stability and Accuracy of Clenshaw-Curtis Collocation. https://arxiv.org/abs/2211.14530

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