@Article{JCM-43-690,
author = {Ma , ZhengHuang , Chengming and Alikhanov , Anatoly A.},
title = {Error Analysis of Fractional Collocation Methods for Volterra Integro-Differential Equations with Noncompact Operators},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {43},
number = {3},
pages = {690--707},
abstract = {<p style="text-align: justify;">This paper is concerned with the numerical solution of Volterra integro-differential
equations with noncompact operators. The focus is on the problems with weakly singular
solutions. To handle the initial weak singularity of the solution, a fractional collocation
method is applied. A rigorous $hp$-version error analysis of the numerical method under
a weighted $H^1$-norm is carried out. The result shows that the method can achieve high
order convergence for such equations. Numerical experiments are also presented to confirm
the effectiveness of the proposed method.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2401-m2023-0196},
url = {http://global-sci.org/intro/article_detail/jcm/23555.html}
}