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.
Singular integral equation Cauchy Kernel Weight function Chebyshev polynomials Weight function
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Articles |
Yazarlar | |
Yayımlanma Tarihi | 22 Mart 2019 |
Gönderilme Tarihi | 20 Ağustos 2018 |
Kabul Tarihi | 22 Ocak 2019 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 1 |
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