Extended Chebyshev Polynomials for Solving Bounded and Unbounded Singular Integral Equations

Autor:	Zainidin K. Eshkuvatov, Bachok M. Taib, Rose Irnawaty Ibrahim, H. Alhawamda
Rok vydání:	2019
Předmět:	History Pure mathematics Chebyshev polynomials Integer Series (mathematics) Bounded function Orthogonal polynomials Spectral properties Extension (predicate logic) Singular integral Computer Science Applications Education Mathematics
Zdroj:	Journal of Physics: Conference Series. 1212:012013
ISSN:	1742-6596 1742-6588
DOI:	10.1088/1742-6596/1212/1/012013
Popis:	In this note, we have developed new classes of one dimensional orthogonal polynomials , namely extended Chebyshev polynomials (ECPs) of the first and second kinds, which are an extension of the Chebyshev polynomials of the first and second kinds respectively. For non-homogeneous SIEs (bounded and unbounded case) truncated series of the first and second kind of ECPs are used to find approximate solution. It is found that first and second kinds of ECPs are orthogonal with weights and , where k is positive odd integer. Spectral properties of first and second kind of ECPs are also proved. Finally, two examples are presented to show the validity and accuracy of the proposed method.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c9809e597d13a9df7dabc852d61a5bb3 https://doi.org/10.1088/1742-6596/1212/1/012013 Zobrazit plný text záznamu