Solution of Singular Integral Equations of the First Kind with Cauchy Kernel

Authors : Subhabrata MONDAL, Bn MANDAL

Pages : 69-74

Doi:10.33434/cams.454740

View : 34 | Download : 7

Publication Date : 2019-03-22

Article Type : Research Paper

Abstract :In this paper an analytic method is developed for solving Cauchy type singular integral equations of the first kind, over a finite interval. Chebyshev polynomials of the first kind, $T_ninsert ignore into journalissuearticles values(x);$, second kind, $U_ninsert ignore into journalissuearticles values(x);$, third kind, $V_ninsert ignore into journalissuearticles values(x);$, and fourth kind, $W_ninsert ignore into journalissuearticles values(x);$, corresponding to respective weight functions $W^{insert ignore into journalissuearticles values(1);}insert ignore into journalissuearticles values(x);=\frac{1}{\sqrt{1-x^2}},W^{insert ignore into journalissuearticles values(2);}insert ignore into journalissuearticles values(x);=\sqrt{1-x^2},W^{insert ignore into journalissuearticles values(3);}insert ignore into journalissuearticles values(x);=\sqrt{\frac{1+x}{1-x}},$ and $~ W^{insert ignore into journalissuearticles values(3);}insert ignore into journalissuearticles values(x);=\sqrt{\frac{1-x}{1+x}}, $ have been used to obtain the complete analytical solutions for four different cases.
Keywords : Singular integral equation, Cauchy Kernel, Weight function, Chebyshev polynomials, Weight function

ORIGINAL ARTICLE URL