Publication: Extended Chebyshev polynomials for solving bounded and unbounded singular integral equations
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Physics Publishing
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.
Description
Keywords
Geometry, Integral equations, Approximate solution, Chebyshev polynomials, Non-homogeneous, Odd integers, Orthogonal polynomial, Second kinds, Singular integral equations, Spectral properties, Polynomials