Chebyshev wavelet method for hypersingular integrals on circles and its applications

Abstract

The numerical algorithm of hypersingular integral is always an important topic in recent years. According to the different definitions of singular integral, we would get the different numerical methods. In this paper, we mainly discuss the approximate value of hypersingular integrals on circle by using the Chebyshev wavelet. A quadrature formula is given by making use of the orthogonality of Chebyshev wavelet and the important formula in generalised function. Then we apply the method to approximate the singular integrals with the Hilert kernel. Two numerical examples are included to demonstrate the validity and applicability of the approach.