The third and fourth kinds of Chebyshev polynomials and best uniform approximation

Eslahchi, M. R.; Dehghan, Mehdi; Amani, Sanaz

doi:10.1016/j.mcm.2011.11.023

Cited by 25 publications

(9 citation statements)

References 4 publications

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“…Further, as for Chebyshev polynomials of all four kinds and Legendre, Laguerre, Fibonacci, and Lucas polynomials, certain sums of finite products of such polynomials are also expressed in terms of all four kinds of Chebyshev polynomials in [5,6,17,18]. Finally, the reader may want to look at [19][20][21] for some applications of Chebyshev polynomials.…”

Section: Introductionmentioning

confidence: 99%

Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials

et al. 2018

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In this paper, we consider sums of finite products of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the previously-studied ones. We represent each of them as linear combinations of Chebyshev polynomials of all kinds whose coefficients involve some terminating hypergeometric functions 2 F 1 . The results may be viewed as a generalization of the linearization problem, which is concerned with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. These representations are obtained by explicit computations.

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Section: Introductionmentioning

confidence: 99%

Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials

et al. 2018

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“…Worthy of note is the fact that many authors have also given numerous and analytical methods for solving Integrodifferential equations. Some examples include; Eslahchi et al (2012) combined the Adomian's decompositions technique with a Wavelet-Galerking approach to solving Integrodifferential Equations. To establish an approximate solution of higher-order linear Fredholm Integrodifferential equations, a realistic matrix technique can be used (Kurt & Sezer, 2008) which possess a constant coefficient beneath the initial boundary condition in phrases of Taylor polynomials, numerical solution of mixed linear Integrodifferential difference equations is considered using the Chebyshev collocation method.…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Approach Using Chebyshev Third Kind Polynomial for Solving Integrodifferential Equations of Higher Order

Abdullahi

James

ISHAQ>

et al. 2022

Gazi University Journal of Science Part A: Engineering and Innovation

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There are several classifications of linear Integral Equations. Some of them include; Voltera Integral Equations, Fredholm Linear Integral Equations, Fredholm-Voltera Integrodifferential. In the past, solutions of higher-order Fredholm-Volterra Integrodifferential Equations [FVIE] have been presented. However, this work uses a computational techniques premised on the third kind Chebyshev polynomials method. The performance of the results for distinctive degrees of approximation (M) of the trial solution is cautiously studied and comparisons have been additionally made between the approximate/estimated and exact/definite solution at different intervals of the problems under consideration. Modelled Problems have been provided to illustrate the performance and relevance of the techniques. However, it turned out that as M increases, the outcomes received after every iteration get closer to the exact solution in all of the problems considered. The results of the experiments are therefore visible from the tables of errors and the graphical representation presented in this work.

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“…To keep the merits of low-order polynomials while overcome their weakness for building surrogate models, the high-order polynomials [23] can be applied to establish surrogate models, such as, the Bernstain polynomials [24,25], Chebyshev polynomials [26,27] and Gegenbauer functions [28].…”

Section: Introductionmentioning

confidence: 99%

Incremental modeling of a new high-order polynomial surrogate model

Luo

Zheng

et al. 2016

Applied Mathematical Modelling

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The third and fourth kinds of Chebyshev polynomials and best uniform approximation

Cited by 25 publications

References 4 publications

Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials

Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials

A New Numerical Approach Using Chebyshev Third Kind Polynomial for Solving Integrodifferential Equations of Higher Order

Incremental modeling of a new high-order polynomial surrogate model

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