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

Abstract

Nurmuhammad et al. developed Sinc-Nystr\"{o}m methods for initial value problems in which solutions exhibit exponential decay end behavior. In the methods, the Single-Exponential (SE) transformation or the Double-Exponential (DE) transformation is combined with the Sinc approximation. Hara and Okayama improved those transformations so that a better convergence rate could be attained, which was afterward supported by theoretical error analyses. However, due to a special function included in the basis functions, the methods have a drawback for computation. To address this issue, Okayama and Hara proposed Sinc-collocation methods, which do not include any special function in the basis functions. This study gives error analyses for the methods.Comment: Keywork: Ordinary differential equations, Initial value problems, Volterra integral equations, Sinc numerical methods, SE transformation, DE transformatio