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.

Keywords:

• Hypersingular integral
• Chebyshev wavelet
• approximate formula
• Hilert kernel
• approximate value

Additional information

Notes on contributors

Y Chen

Yiming Chen obtained his Doctorate from Yanshan University. He has been a post-doctoral student from 2005 to 2007 in Glamorgan University, United Kingdom. He is now a Professor in the College of Science, Yanshan University, China. His research interests include boundary element method in contact problem, boundary element solution for the variation inequality, and numerical solution of differential equations.

M Yi

Mingxu Yi obtained his Bachelors degree from Jinan University. He is now a Masters student in the College of Sciences, Yanshan University, China. His research interests include approximate solution of supersingular integral in natural boundary element method, and numerical solution of fractional differential equations.

C Chen

Chen Chen obtained her Bachelors degree from Italy. She is now a Masters student at Yanshan University, China. She is also working in the Department of Italian, China Radio International, China. Her research interests include approximate solution of supersingular integral in natural boundary element method, and numerical solution of fractional differential equations.