Operational Matrices of Derivative and Product for Shifted Chebyshev Polynomials of Type Three

Samaa Fouad, Suha SHIHAB


In this paper an explicit expression for constructing operational matrices of derivative  and product based on shifted chebyshev polynomials of type three are first presented. Then the conversion of power form basis to shifted chebyshev polynomials of the type three is listed through this work.


Operational matrix of derivative; Operational matrix of product; Shifted chebyshev polynomials of type three

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S. N. Shihab, M. A. Sarhan, Convergence analysis of shifted fourth kind Chebyshev wavelets, IOSR journal of mathematics, 10 (2) (2014) 54-58.

T. Kim, D.S. Kim, D.V. Dolgy, J. Kwon, Sums of finite products of Chebyshev polynomials of the third and fourth kinds, Adv Differ Equ. 2018 (2018) 283.

A. Tatarczak, An Extension of the Chebyshev Polynomials, Complex Anal. Oper. Theory. 10 (2016) 1519–1533.

S. N. Al-Rawi, NUMERICAL SOLUTION OF INTEGRAL EQUATIONS USING TAYLOR SERIES, Journal of the College of Education, 5 (1992) 51-60.

M. N. Sahlan, H. Feyzollahzadeh, Operational matrices of Chebyshev polynomials for solving singular Volterra integral equations, Math Sci. 11 (2017) 165–171.

Z. Yang, H. Zhang, Chebyshev polynomials for approximation of solution of fractional partial differential equations with variable coefficients, in: Atlantis Press, (IC3ME 2015) (2015) 252-260.

W. Siyi, Some new identities of Chebyshev polynomials and their applications, Adv Differ Equ. (2015) 355 1-8.

F. Dkhilalli, S. M. Borchani, M. Rasheed, R. Barille, S. Shihab, K. Guidara, M Megdiche, Characterizations and morphology of sodium tungstate particles, Royal Society open science, 5 (8) (2018) 1-16.

S. N. Al-Rawi, F. A. Al-Heety, S. S. Hasan, A New Computational Method for Optimal Control Problem with B-spline Polynomials, Engineering and Technology Journal, 28 (18) (2010) 5711-5718.

S. N. Al-Rawi, H. R. Al-Rubaie, An Approximate solution of some continuous time Linear-Quadratic optimal control problem via Generalized Laguerre Polynomial, Journal of Pure and Applied Sciences, 22 (1) (2010) 85-97.

J. A. Eleiwy, S. N. Shihab, Chebyshev Polynomials and Spectral Method for Optimal Control Problem, Engineering and Technology Journal, 27 (14) (2009) 2642-2652.

I. N. Ahmed Fahmi, S. F. Ibraheem, E. H. Ouda, Indirect Method for Optimal Control Problem Using Boubaker Polynomial, Baghdad Science Journal, 13 (1) (2016) 183-189.

E. H. Ouda, An Approximate Solution of some Variational Problems Using Boubaker Polynomials, Baghdad Science Journal, 5 (1) (2018) 106-109.

E. H. Ouda, A new Approach for Solving Optimal Control Problems Using Normalized Boubaker Polynomials, Emirates Journal for Engineering Research, 23 (1) (2018) 1-12.

S. N. SHIHAB, M. A. Sarhan, New Operational Matrices of Shifted Fourth Chebyshev wavelets, Elixir International Journal-Applied Mathematics, 69 (1) (2014) 23239-23244.

S. N. Shihab, T. N. Naif, On the orthonormal Bernstein polynomial of order eight, open Science Journal of Mathematics and Application, 2 (2) (2014) 15-19.

Maha Delphi, Suha SHIHAB, Operational Matrix Basic Spline Wavelets of Derivative for linear Optimal Control Problem, Electronics Science Technology and Application 6 (2), 18-24.

DOI: http://dx.doi.org/10.18686/esta.v6i2.90


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