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

Year 2019, Volume: 2 Issue: 1, 69 - 74, 22.03.2019

Subhabrata Mondal , B.n. Mandal

https://doi.org/10.33434/cams.454740

Cited By: 6

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, $T_n(x)$, second kind, $U_n(x)$, third kind, $V_n(x)$, and fourth kind, $W_n(x)$, corresponding to respective weight functions $W^{(1)}(x)=\frac{1}{\sqrt{1-x^2}},W^{(2)}(x)=\sqrt{1-x^2},W^{(3)}(x)=\sqrt{\frac{1+x}{1-x}},$ and $~ W^{(3)}(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

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