Discontinuous Galerkin approximations to second-kind Volterra integral equations with weakly singular kernel

被引：12

作者：

Liang, Hui ^{[1
]}

机构：

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

来源：

APPLIED NUMERICAL MATHEMATICS | 2022年 / 179卷

关键词：

Volterra integral equations; Weakly singular kernels; Discontinuous Galerkin methods; Convergence; Graded meshes; CONVERGENCE;

D O I：

10.1016/j.apnum.2022.04.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The discontinuous Galerkin (DG) method is employed to solve second-kind Volterra integral equations (VIEs) with weakly singular kernels. It is proved that the quadrature DG (QDG) method obtained from the DG method by approximating the inner products by suitable numerical quadrature formulas, is equivalent to the piecewise discontinuous polynomial collocation method. The convergence theory is established for VIEs for both uniform and graded meshes. Some numerical experiments are given to illustrate the obtained theoretical results. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：170 / 182

页数：13

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