Numerical Quadratures for Hadamard Hypersingular Integrals
Youjian Shen 1*1 Department of Mathematics, Hainan Normal University, Haikou 571158, China/Department of Mathematics, Zhongshan University, Guangzhou 510275, China.
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 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 accuracy of the approximation results are satisfactory. Moreover, the rate and the accuracy can be improved by choosing appropriate weight functions.
Key words: Gaussian quadrature; finite part; hypersingular integral; orthonormal polynomial.
AMS subject classifications: 65D30,65D32