APPROXIMATIONS OF HYPERSINGULAR INTEGRALS FOR NEGATIVE FRACTIONAL EXPONENT  

作　　者：Chaolang Hu Tao Lu 

机构地区：[1]College of Mathematics, Sichuan University, Chengdu 610064, China

出　　处：《Journal of Computational Mathematics》2018年第5期627-643,共17页计算数学（英文）

基　　金：This work was supported by National Natural Science Foundation of China （Grant NO. 91430105 and Grant NO. 11771312）.

摘　　要：This article presents approximations of the hypersingular integrals fa^b g（x）（x- t）^adx and fa^b g（x）｜x- t｜dx with arbitrary singular point t C （a, b） and negative fraction number 〈 -1. These general expansions are applicable to a large range of hypersingular inte- grals, including both popular hypersingular integrals discussed in the literature and other important ones which have not been addressed yet. The corresponding mid-rectangular formulas and extrapolations, which can be calculated in fairly straightforward ways, are investigated. Numerical examples are provided to illustrate the features of the numerical methods and verify the theoretical conclusions.This article presents approximations of the hypersingular integrals fa^b g（x）（x- t）^adx and fa^b g（x）｜x- t｜dx with arbitrary singular point t C （a, b） and negative fraction number 〈 -1. These general expansions are applicable to a large range of hypersingular inte- grals, including both popular hypersingular integrals discussed in the literature and other important ones which have not been addressed yet. The corresponding mid-rectangular formulas and extrapolations, which can be calculated in fairly straightforward ways, are investigated. Numerical examples are provided to illustrate the features of the numerical methods and verify the theoretical conclusions.

关 键 词：Hypersingular integral Negative fractional exponent Mid-rectangular quadrature formula Extrapolation. 

分 类 号：O172.2[理学—数学] TU-092[理学—基础数学]