Quadrature methods for 2D and 3D problems

被引：9
|
作者：
Rathsfeld, A [1 ]
机构：
[1] Weierstr Inst Angew Anal & Stochast, D-10117 Berlin, Germany
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2000年 / 125卷 / 1-2期
关键词：
D O I：
10.1016/S0377-0427(00)00484-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we give an overview on well-known stability and convergence results for simple quadrature methods based on low-order composite quadrature rules and applied to the numerical solution of integral equations over smooth manifolds. First, we explain the methods for the case of second-kind equations. Then we discuss what is known for the analysis of pseudodifferential equations. We explain why these simple methods are not recommended for integral equations over domains with dimension higher than one. Finally, for the solution of a two-dimensional singular integral equation, we prove a new result on a quadrature method based on product rules. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：439 / 460
页数：22
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