小波法求一类强奇异积分近似值  

Wavelet method for solving approximate solution of a class of hypersingular integral

作　　者：徐琳[1] 尹建华[1] 李秀云[1] 

机构地区：[1]河北民族师范学院数学与计算机系,河北承德067000

出　　处：《辽宁工程技术大学学报（自然科学版）》2013年第5期697-700,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：河北省自然科学基金资助项目(A2011205092)

摘　　要：针对一类强奇异积分,给出了Hadamard有限部分积分的定义,并通过Legendre小波求其近似值.由于Legendre小波具有正交性、小支集性和小波函数的可计算性,因此利用Legendre小波近似给定函数,将原来区间转化为若干子区间,当奇异点位于某一子区间时,可采用所给强奇异积分的Hadamard有限部分积分定义来求值.给出了算法的误差估计,通过数值算例进一步验证方法的有效性和理论的正确性.This paper discussed a class of hypersingular, specified the definition of Hadamard finite-part integral of the integral, and studied its approximate solution by using Legendre wavelet. Since Legendre wavelet has a better orthogonality, good explicit expression and computability of the wavelet function, the given function can be approximated by using the Legendre wavelet. Transforming the initial interval into many subintervals when the singular point is located in some subinterval, this study computed the hypersingular integral by adopting the definition of Hadamard finite-part integral. Error estimate is also obtained in this study. The feasibility of the method and the correctness of the theorem are verified by the numerical examples.

关 键 词：强奇异积分 有限部分积分 奇异点 LEGENDRE小波 正交性 子区间 误差估计 近似值 

分 类 号：O241.8[理学—计算数学]