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

Subhabrata MONDAL; B.n. MANDAL

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

Makale detayları

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

Yazarlar:

Subhabrata MONDAL | B.n. MANDAL

Yayıncı:

Emrah Evren KARA

Ana Başlıklar:

Matematik

Dergi:

Communications in Advanced Mathematical Sciences 2019 Vol.2 Issue 1, pp.69-74

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000911735

Sıklık:

Üç Aylık

pISSN:

2651-4001

DOI:

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

Özet:

 


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, Tn(x)Tn(x)T_n(x), second kind, Un(x)Un(x)U_n(x), third kind, Vn(x)Vn(x)V_n(x), and fourth kind, Wn(x)Wn(x)W_n(x), corresponding to respective weight functions W(1)(x)=1√1−x2,W(2)(x)=√1−x2,W(3)(x)=√1+x1−x,W(1)(x)=11−x2,W(2)(x)=1−x2,W(3)(x)=1+x1−x,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)=√1−x1+x, W(3)(x)=1−x1+x,~ W^{(3)}(x)=\sqrt{\frac{1-x}{1+x}},  have been used to obtain the complete analytical solutions for four different cases.

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Makale detayları

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

Yazarlar: Subhabrata MONDAL | B.n. MANDAL

Yayıncı: Emrah Evren KARA

Ana Başlıklar: Matematik

Dergi: Communications in Advanced Mathematical Sciences 2019 Vol.2 Issue 1, pp.69-74

Belge Tipi: Makale

Yayın Tarihi: 3/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000911735

Sıklık: Üç Aylık

pISSN: 2651-4001

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

Sayı

Yazarlar:

Subhabrata MONDAL | B.n. MANDAL

Yayıncı:

Emrah Evren KARA

Ana Başlıklar:

Matematik

Dergi:

Communications in Advanced Mathematical Sciences 2019 Vol.2 Issue 1, pp.69-74

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000911735

Sıklık:

Üç Aylık

pISSN:

2651-4001

DOI:

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