We discuss Lagrange interpolation on two sets of nodes in two dimensions where the coordinates of the nodes are Chebyshev points having either the same or opposite parity. We use a formula of Xu for Lagrange polynomials to obtain a general interpolation theorem for bivariate polynomials at either set of Chebyshev nodes. An extra term must be added to the interpolation formula to handle all poly...

We give two recursive expressions for both MacWilliams and Chebyshev matrices. The expressions give rise to simple recursive algorithms for constructing the matrices. In order to derive the second recursion for the Chebyshev matrices we find out the Krawtchouk coefficients of the Discrete Chebyshev polynomials, a task interesting on its own.

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

In this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which will be used to convert the system of integral equations into a system of algebraic equations. Also, the error is analyzed and ...

The normal mode model is one of the most popular approaches for solving underwater sound propagation problems. Among other methods, finite difference method widely used in classic programs. In many recent studies, spectral has been discretization. It generally more accurate than method. However, requires that variables to be solved are continuous space, and traditional powerless a layered marin...

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

‎This paper provides the fractional derivatives of‎ ‎the Caputo type for the sinc functions‎. ‎It allows to use efficient‎ ‎numerical method for solving fractional differential equations‎. ‎At‎ ‎first‎, ‎some properties of the sinc functions and Legendre‎ ‎polynomials required for our subsequent development are given‎. ‎Then‎ ‎we use the Legendre polynomials to approximate the fractional‎ ‎deri...

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...

In this paper, a method based on Chebyshev polynomials is developed for examination of geometrically nonlinear behaviour of thin rectangular composite laminated plates under end-shortening strain. Different boundary conditions and lay-up configurations are investigated and classical laminated plate theory is used for developing the equilibrium equations. The equilibrium equations are solved dir...