ON THE CONVERGENCE OF DISCONTINUOUS GALERKIN METHODS FOR INTEGRAL-ALGEBRAIC EQUATIONS OF INDEX

被引：0

作者：

Gao, Hecong ^{[1
]}

Liang, Hui ^{[1
]}

机构：

[1] Harbin Inst Technol, Sch Sci, Shenzhen 518055, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2024年 / 29卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Integral-algebraic equation; index-1; discontinuous Galerkin method; convergence; superconvergence; NUMERICAL-SOLUTION;

D O I：

10.3934/dcdsb.2023168

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. The integral-algebraic equation (IAE) of index 1 is a mixed system of first-kind and second-kind Volterra integral equations (VIEs). In this paper, the discontinuous Galerkin (DG) method is proposed to solve the index-1 IAE, and the optimal global convergence order is obtained. The iterated DG method is introduced in order to improve the numerical accuracy, and the global superconvergence of the iterated DG solution is derived. However, due to the lack of the local superconvergence of the DG residual for first-kind VIEs, there is no local superconvergence for the mixed IAE system of first-kind and secondkind VIEs, and the numerical experiments also verify this. Some numerical experiments are given to illustrate the obtained theoretical results.

引用

页码：2092 / 2109

页数：18

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