摘要
In this paper,we develop Gaussian quadrature formulas for the Hadamard fi- nite part integrals.In our formulas,the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f(x)so that the Gaussian quadrature formulas have degree n-1.The error estimates of the formulas are obtained.It is found from the numerical examples that the convergence rate and the accu- racy of the approximation results are satisfactory.Moreover,the rate and the accuracy can be improved by choosing appropriate weight functions.
In this paper, we develop Caussian quadrature formulas for the Hadamard finite part integrals. In our formulas, the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f（x） so that the Caussian quadrature formulas have degree n - 1. The error estimates of the formulas are obtained. It is found from the numerical examples that the convergence rate and the accuracy of the approximation results are satisfactory. Moreover, the rate and the accuracy can be improved by choosing appropriate weight functions.
基金
This research is supported in part by China NSF under grant 10071096
NSF of Guangdong under grant 990228
NSF of Hainan under grant 80525
the One Hundred Distinguished Young Chinese Scientists Program of the Chinese Academy of Sciences from Yuesheng Xu.
关键词
数值积分
有限部分
规格化正交多项式
求积公式
Gaussian quadrature
finite part
hypersingular integral
orthonormal polynomial.
