Mathematics and Statistics Vol. 8(2), pp. 106 - 120
DOI: 10.13189/ms.2020.080206
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Semi Bounded Solution of Hypersingular Integral Equations of the First Kind on the Rectangle

Zainidin Eshkuvatov ^1,*, Massamdi Kommuji ¹, Rakhmatullo Aloev ², Nik Mohd Asri Nik Long ³, Mirzoali Khudoyberganov ^2
1 Faculty of Science and Technology, Universiti Sains Islam Malaysia, Malaysia
² Faculty of Mathematics, National University of Uzbekistan, Uzbekistan
³ Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Malaysia

ABSTRACT

A hypersingular integral equations (HSIEs) of the first kind on the interval [ 1 ; 1 ] with the assumption that kernel of the hypersingular integral is constant on the diagonal of the domain is considered. Truncated series of Chebyshev polynomials of the third and fourth kinds are used to find semi bounded (unbounded on the left and bounded on the right and vice versa) solutions of HSIEs of first kind. Exact calculations of singular and hypersingular integrals with respect to Chebyshev polynomials of third and forth kind with corresponding weights allows us to obtain high accurate approximate solution. Gauss-Chebyshev quadrature formula is extended for regular kernel integrals. Three examples are provided to verify the validity and accuracy of the proposed method. Numerical examples reveal that approximate solutions are exact if solution of HSIEs is of the polynomial forms with corresponding weights.

KEYWORDS
Approximation, Chebyshev polynomials, Convergence, Hypersingular integral equations

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Zainidin Eshkuvatov , Massamdi Kommuji , Rakhmatullo Aloev , Nik Mohd Asri Nik Long , Mirzoali Khudoyberganov , "Semi Bounded Solution of Hypersingular Integral Equations of the First Kind on the Rectangle," Mathematics and Statistics, Vol. 8, No. 2, pp. 106 - 120, 2020. DOI: 10.13189/ms.2020.080206.

(b). APA Format:
Zainidin Eshkuvatov , Massamdi Kommuji , Rakhmatullo Aloev , Nik Mohd Asri Nik Long , Mirzoali Khudoyberganov (2020). Semi Bounded Solution of Hypersingular Integral Equations of the First Kind on the Rectangle. Mathematics and Statistics, 8(2), 106 - 120. DOI: 10.13189/ms.2020.080206.