Adv. Appl. Math. Mech., 17 (2025), pp. 1867-1894.
Published online: 2025-09
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2025-0147}, url = {http://global-sci.org/intro/article_detail/aamm/24498.html} }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.