Theoretical analysis of Sinc-collocation methods and Sinc-Nystr\"{o}m methods for initial value problems

TL;DR

This paper extends the theoretical analysis of Sinc-collocation and Sinc-Nyström methods for initial value problems to systems of equations, proposing a more efficient variable transformation and confirming its effectiveness through analysis and numerical experiments.

Contribution

It introduces a more efficient variable transformation for Sinc-collocation methods and extends theoretical results to systems of equations, enhancing computational efficiency.

Findings

The new Sinc-collocation method is more efficient computationally.

Theoretical analysis confirms the improved efficiency.

Numerical experiments support the theoretical results.

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.