一类含Hilbert核的奇异积分方程的直接解法  

The direct method of solution for a class of singular integral equations with Hilbert kernel

作　　者：李凯雅 刘华[1] 魏鑫 屈非非[1] LI Kaiya;LIU Hua;WEI Xin;QU Feifei(School of Science,Tianjin University of Technology and Education,Tianjin 300222;School of Science,Xi′an Shiyou University,Xi′an Shaanxi 710065)

机构地区：[1]天津职业技术师范大学理学院,天津300222 [2]西安石油大学理学院,陕西西安710065

出　　处：《宁夏师范学院学报》2021年第1期35-44,共10页Journal of Ningxia Normal University

基　　金：Scientific research project of Tianjin municipal education commission(2017KJ118).

摘　　要：讨论具有Hilbert核的奇异积分方程的直接解法.遵循Cauchy核奇异积分方程直接解法的路线,首先给出了周期形式推广的留数定理和Plemelj公式,然后在不对奇异积分进行数值离散的情况下直接将具有Hilbert核的奇异积分方程转化为代数方程,最后证明了代数方程与原方程等价.The direct method of solution for singular integral equations with Hilbert kernel is discussed in this paper.Following the route of the direct method of solution for singular integral equations with Cauchy kernel,the generalized residue theorem and Plemelj formula in periodic form are stated.Then the singular integral equation with Hilbert kernel is directly transformed into an algebraic equation without the numerical discretization of the singular integral.At last the equivalence between algebraic equation and original equation is proved.

关 键 词：HILBERT核 奇异积分方程 推广的留数定理 PLEMELJ公式 直接解法 

分 类 号：O17[理学—基础数学]