Chebyshev polynomial solution of the system of Cauchy-type singular integral equations of the first kind

Abstract

This paper presents a Chebyshev series method for the numerical solutions of system of the first kind Cauchy type singular integral equation (SIE). The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density functions. It is shown that the numerical solution of system of characteristic SIEs is identical to the exact solution when the force functions are cubic functions.

Keywords:

• singular integral equation
• characteristic singular integral equation
• Chebyshev polynomials
• Chebyshev series expansion
• approximate technique

2010 AMS Subject Classifications:

• 45E05
• 41A55

Acknowledgements

The authors thank the referee for carefully reading the manuscript and providing constructive comments.