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Title: | A new class of orthogonal polynomials for solving logarithmic singular integral equations | Authors: | Alhawamda H. Taib B.M. Eshkuvatov Z.K. Ibrahim R.I. |
Keywords: | Chebyshev polynomials;New orthogonal basis functions;Singular integral | Issue Date: | 2020 | Publisher: | Ain Shams University | Journal: | Ain Shams Engineering Journal | Abstract: | In this note, we propose a new class of orthogonal polynomials (named Bachok–Hasham polynomials H1nk(x)), which is an extension of the Chebyshev polynomials. Eigenfunctions and corresponding eigenvalues are found for the homogeneous second kind of Logarithmic Singular Integral Equations (LogSIEs). For non-homogeneous LogSIEs truncated series of the first kind Bachok–Hasham polynomials are used to find approximate solution. It is found that first kind of Bachok–Hasham polynomials (H1nk(x)) are orthogonal with weight [Formula presented], where k is positive odd integer. Properties of first kind of Bachok–Hasham polynomials are also proved. Finally, two examples are presented to show the validity and accuracy of the proposed method. © 2019 THE AUTHORS |
Description: | Ain Shams Engineering Journal 11 (2020) 489–494 |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075860777&doi=10.1016%2fj.asej.2017.10.010&partnerID=40&md5=2ebe28bb81006c5682236373109dc697 https://www.sciencedirect.com/science/article/pii/S2090447919301340 |
ISSN: | 20904479 | DOI: | https://doi.org/10.1016/j.asej.2017.10.010 |
Appears in Collections: | Scopus |
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