@Article{AAMM-17-1867,
author = {Zhang , Haiyan and Liang , Hui},
title = {On Convergence and Superconvergence of  Discontinuous Galerkin Method for Semi-Explicit Index-1 Integro-Differential Algebraic Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2025},
volume = {17},
number = {6},
pages = {1867--1894},
abstract = {<p style="text-align: justify;">This paper mainly focuses on the discontinuous Galerkin (DG) method for
 solving the semi-explicit index-1 integro-differential algebraic equation (IDAE), which
 is a coupled system of Volterra integro-differential equations (VIDEs) and second-kind
 Volterra integral equations (VIEs). The DG approach is applied to both the VIDE and
 VIE components of the system. The global convergence respectively in the $L^2$- norm
 and $L^\infty$-norm is established, and the local superconvergence for VIDE component is
 obtained. Furthermore, numerical examples are presented to validate the theoretical
 convergence and superconvergence results.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2025-0147},
url = {http://global-sci.org/intro/article_detail/aamm/24498.html}
}