Abstract The main aim of the current paper is to construct a numerical algorithm for solutions second-order linear and nonlinear differential equations subject Robin boundary conditions. A basis function in terms shifted Chebyshev polynomials first kind that satisfy homogeneous conditions constructed. It has established operational matrices derivatives constructed polynomials. obtained are spec...

In this paper, we firstly present a general expression for the entries of the th r   N r power of certain -square n are complex tridiagonal matrix, in terms of the Chebyshev polynomials of the first kind. Secondly, we obtain two complex factorizations for Fibonacci and Pell numbers. We also give some Maple 13 procedures in order to verify our calculations.

In this study, we deal with an $m$ banded circulant matrix, generally called $m$-diagonal matrix. This special family of matrices arise in many applications such as prediction, time series analysis, spline approximation, difference solution partial differential equations, and so on. We firstly obtain the statements eigenvalues eigenvectors matrix based on Chebyshev polynomials first second kind...

1. R. L. Adler & T. J. Rivlin. "Ergodic and Mixing Properties of Chebyshev Polynomials." Proa. Amer. Math. Soc. 15 (1964) :79'4-7'96. 2. P. Johnson & A. Sklar. "Recurrence and Dispersion under Iteration of Cebysev Polynomials." To appear. 3. C.H. Kimberling. "Four Composition Identities for Chebyshev Polynomials." This issue, pp. 353-369. 4. T. J. Rivlin. The Chebyshev Polynomials. New York: Wi...

Tthis paper, is concerned with obtaining numerical solutions for a class of convection-diffusion equations (CDEs) with variable coefficients. Our approaches are based on collocation methods. These approaches implementing all four kinds of shifted Chebyshev polynomials in combination with Sinc functions to introduce an approximate solution for CDEs . This approximate solution can be expressed as...