TY - JOUR
T1 - On Convergence and Superconvergence of  Discontinuous Galerkin Method for Semi-Explicit Index-1 Integro-Differential Algebraic Equations
AU - Zhang , Haiyan
AU - Liang , Hui
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1867
EP - 1894
PY - 2025
DA - 2025/09
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2025-0147
UR - https://global-sci.org/intro/article_detail/aamm/24498.html
KW - Integro-differential algebraic equations, index 1, DG method, convergence, superconvergence.
AB - <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>