Publication: A new class of orthogonal polynomials for solving logarithmic singular integral equations
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Date
2020
Journal Title
Journal ISSN
Volume Title
Publisher
Ain Shams University
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
Keywords
Chebyshev polynomials, New orthogonal basis functions, Singular integral