@Article{JCM-31-47,
author = {Yanping Chen, Xianjuan Li and Tao Tang},
title = {A Note on Jacobi Spectral-Collocation Methods for Weakly Singular Volterra Integral Equations with Smooth Solutions},
journal = {Journal of Computational Mathematics},
year = {2013},
volume = {31},
number = {1},
pages = {47--56},
abstract = {<p style="text-align: justify;">This work is concerned with spectral Jacobi-collocation methods for Volterra integral equations of the second kind with a weakly singular of the form $(t-s)^{-\alpha}$. When the underlying solutions are sufficiently smooth, the convergence analysis was carried out in [Chen &amp; Tang, J. Comput. Appl. Math., 233 (2009), pp. 938-950]; due to technical reasons the results are restricted to $0&lt;\mu&lt;\frac{1}{2}$. In this work, we will improve the results to the general case $0&lt;\mu&lt;1$ and demonstrate that the numerical errors decay exponentially in the infinity and weighted norms when the smooth solution is involved.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1208-m3497},
url = {http://global-sci.org/intro/article_detail/jcm/9720.html}
}