Approximation of derivatives over the finite interval via the Sinc approximation combined with the DE transformation and its theoretical error analysis

抄録

Lundin and Stenger applied the Sinc approximation combined with the single-exponential (SE) transformation to approximate derivatives over the finite interval (−1,1), and provided its theoretical error analysis. In this study, we improve their approximation formula by replacing the SE transformation with the double-exponential (DE) transformation. The replacement has already been proposed for the first-order derivative, and an error analysis has also been provided. This study proposes the approximation and provides its rigorous convergence analysis for any order derivative.