二维弱奇异积分高精度数值求积公式的构造  

A New Construction of High Accurate Numerical Quadrature Formulas for 2D Weak Singular Integral

作　　者：曾光[1] 黄晋[2] 雷莉[1] 宁德圣 

机构地区：[1]东华理工大学理学院,江西南昌330013 [2]电子科技大学数学科学学院,四川成都611731

出　　处：《东华理工大学学报（自然科学版）》2014年第4期447-450,共4页Journal of East China University of Technology(Natural Science)

基　　金：国家自然基金(11301070);江西省自然科学基金(20132BAB211016);江西省教育厅科技项目(GJJ13444);东华理工大学博士启动基金

摘　　要：在欧拉—麦克劳林展开式和一维弱奇异积分的求积公式的基础上,推导出了二维弱奇异积分的求积公式及其误差的渐进展开式。此类求积公式只需赋值,不需计算二重积分,故计算量小。利用这类积分公式进行计算可以得到十分精确的结果,使得收敛阶大为提高,为讨论更为复杂地多维弱奇异积分方程奠定了基础。Quadrature formulas for the Two-dimension weak singular integrals are presented,and the asymptotic expansions of the errors are also obtained by Euler-Maclaurin expansions and one-dimension weak singular quadrature formulas.The algorithms are very simple and straightforward for calculating singular integrals.These quadrature formulas contain no calculation of any double integration,and computation costs are reduced greatly but the accuracy order of the algorithms improved obviously.Using the quadrature formulas can obtain accurate results,which provide possibilities for solving more complicated multi-dimension weak singular integrals.

关 键 词：弱奇异积分 求积公式 高精度 欧拉—麦克劳林展开式 

分 类 号：O186[理学—数学]