TY  - JOUR
AU  - Abdulkawi, M. 
AU  - Eshkuvatov, Z. K. 
AU  - Long, N.M.A. Nik 
PY  - 2011
TI  - Half-bounded Numerical Solution of Singular Integral Equations with Cauchy Kernel
JF  - Journal of Mathematics and Statistics
VL  - 7
IS  - 1
DO  - 10.3844/jmssp.2011.81.85
UR  - https://thescipub.com/abstract/jmssp.2011.81.85
AB  - Problem statement: In this study, a numerical solution for singular integral equations of
the first kind with Cauchy kernel over the finite segment [-1,1] is presented. The numerical solution is
bounded at x =1 and unbounded at x = -1. Approach: The numerical solution is derived by approximating
the unknown density function using the weighted Chebyshev polynomials of the fourth kind. Results: The
force function is approximated by using the Chebyshev polynomials of the third kind. Conclusion: The
exactness of the numerical solution is shown for characteristic equation when the force function is a cubic.