2023/06/27 by Tomoaki Okayama, Okayama, Tomoaki, Ryota Hara +3
Computer Science · Mathematics · #65D30 #65L04 #65L05 #65R20 #FOS: Mathematics #Fractional Differential Equations Solutions #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2306.15175
openalex publication_date 2023/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nurmuhammad et al. developed the Sinc-Nyström 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.