Semi Bounded Solution of Hypersingular Integral Equations of the First Kind on the Rectangle

Autor:	Massamdi Kommuji, N. M. A. Nik Long, Rakhmatullo Aloev, Zainidin K. Eshkuvatov, Mirzoali Khudoyberganov
Rok vydání:	2020
Předmět:	Statistics and Probability Economics and Econometrics Chebyshev polynomials Bounded function Diagonal Applied mathematics Rectangle Statistics Probability and Uncertainty Approximate solution Integral equation Mathematics::Numerical Analysis Quadrature (mathematics) Mathematics
Zdroj:	Mathematics and Statistics. 8:106-120
ISSN:	2332-2144 2332-2071
DOI:	10.13189/ms.2020.080206
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::baf5e92b595dd91c79b60002b6701722 https://doi.org/10.13189/ms.2020.080206 Zobrazit plný text záznamu