Theoretical analysis of Sinc-collocation methods and Sinc-Nystr\"{o}m methods for initial value problems
Abstract
A Sinc-collocation method has been proposed by Stenger, and he also gave theoretical analysis of the method in the case of a `scalar' equation. This paper extends the theoretical results to the case of a `system' of equations. Furthermore, this paper proposes more efficient method by replacing the variable transformation employed in Stenger's method. The efficiency is confirmed by both of theoretical analysis and numerical experiments. In addition to the existing and newly-proposed Sinc-collocation methods, this paper also gives similar theoretical results for Sinc-Nystr\"{o}m methods proposed by Nurmuhammad et al. From a viewpoint of the computational cost, it turns out that the newly-proposed Sinc-collocation method is the most efficient among those methods.
Cite
@article{arxiv.1304.6508,
title = {Theoretical analysis of Sinc-collocation methods and Sinc-Nystr\"{o}m methods for initial value problems},
author = {Tomoaki Okayama},
journal= {arXiv preprint arXiv:1304.6508},
year = {2022}
}
Comments
Keywords: Sinc approximation, Sinc indefinite integration, differential equation, Volterra integral equation, tanh transformation, double-exponential transformation