Error analyses of Sinc-collocation methods for exponential decay initial value problems

TL;DR

This paper analyzes the error behavior of Sinc-collocation methods designed for initial value problems with solutions that decay exponentially, focusing on their convergence and computational advantages.

Contribution

It provides a detailed error analysis of Sinc-collocation methods that avoid special functions, improving understanding of their accuracy and efficiency.

Findings

Error bounds for Sinc-collocation methods established

Methods show improved computational efficiency over previous approaches

Theoretical convergence rates confirmed through analysis

Abstract

Nurmuhammad et al. developed the Sinc-Nystr\"{o}m methods for initial value problems in which the solutions exhibit exponential decay end behavior. In these methods, the Single-Exponential (SE) transformation or the Double-Exponential (DE) transformation is combined with the Sinc approximation. Hara and Okayama improved on these transformations to attain a better convergence rate, which was later supported by theoretical error analyses. However, these methods have a computational drawback owing to the inclusion of a special function in the basis functions. To address this issue, Okayama and Hara proposed Sinc-collocation methods, which do not include any special function in the basis functions. This study conducts error analyses of these methods.