Novel Expressions for the Derivatives of Sixth Kind Chebyshev Polynomials: Spectral Solution of the Non-Linear One-Dimensional Burgers’ Equation

This paper is concerned with establishing novel expressions that express the derivative of any order orthogonal polynomials, namely, Chebyshev polynomials sixth kind in terms themselves. We will prove these involve certain terminating hypergeometric functions type 4F3(1) can be reduced some specific cases. The derived along linearization formula serve obtaining a numerical solution non-linear one-dimensional Burgers’ equation based on application spectral tau method. Convergence analysis proposed double shifted expansion investigated. Numerical results are displayed aiming to show efficiency and applicability algorithm.