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  1. Home
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  4. Extended Chebyshev polynomials for solving bounded and unbounded singular integral equations
 
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Extended Chebyshev polynomials for solving bounded and unbounded singular integral equations

Journal
Open Access
J. Phys. Conf. Ser.
Date Issued
2019
Author(s)
Alhawamda H.
Eshkuvatov Z.K.
Taib B.M.
Ibrahim R.I.
DOI
10.1088/1742-6596/1212/1/012013
Abstract
In this note, we have developed new classes of one dimensional orthogonal polynomials Zk(i,n)(x),i = {1,2},n = 0,1,2,..., 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 Zk(in)(x),i = {1,2} are orthogonal with weights w(1,k)(x)= xk-1/1-x2k and w(2,k)(x) = xk-11-x2k, 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.
Subjects

Geometry

Integral equations

Approximate solution

Chebyshev polynomials...

Non-homogeneous

Odd integers

Orthogonal polynomial...

Second kinds

Singular integral equ...

Spectral properties

Polynomials

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Extended Chebyshev polynomials for solving bounded and unbounded singular integral equations.pdf

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