Chebyshev小波求解超奇异积分

Chebyshev wavelets for solving hyper-singular integral

针对超奇异积分的数值计算问题.利用Chebyshev小波计算基于Hadamard有限部分积分定义的超奇异积分.由于Chebyshev小波有正交性、显式表达式及小波函数的可计算性,可以将超奇异积分区间内的奇异点变换到区间端点处,再通过区间端点处Hadamard有限部分积分的定义来计算超奇异积分.算例表明了该方法具有有效性和可行性.

In terms of the hyper-singular integrals numerical calculation problems,this paper uses the Chebyshev wavelets to calculate the hyper-singular integrals which are based on the definition of Hadamard finite-part integrals of the hyper-singular integrals.As the Chebyshev wavelet has the properties of orthogonality,the explicit expression and the computability of wavelet function,the singular point in the hyper-singular interval can be transformed into the endpoints of interval,and subsequently,the hyper-singular integral can be computed by using the definition of Hadamard finite-part integral where the hyper-singular point is located at the endpoints of interval.The study examples demonstrate the validity and applicability of the proposed technique.