Error analyses of Sinc-collocation methods for exponential decay initial value problems
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.
Cite
@article{arxiv.2306.15175,
title = {Error analyses of Sinc-collocation methods for exponential decay initial value problems},
author = {Tomoaki Okayama and Ryota Hara and Shun'ichi Goto},
journal= {arXiv preprint arXiv:2306.15175},
year = {2025}
}
Comments
Keywork: Ordinary differential equations, Initial value problems, Volterra integral equations, Sinc numerical methods, SE transformation, DE transformation