In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

presents a modiied Chebyshev pseudospec-tral method, involving mapping of the Chebyshev points, for solving rst-order hyperbolic initial boundary value problems. It is conjectured that the time step restriction for the modiied method is O(N ?1) compared to O(N ?2) for the standard Chebyshev pseudospectral method, where N is the number of discretization points in space. In the present paper we s...

In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency...

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...

We analyze the asymptotic rates of convergence of Chebyshev, Legendre and Jacobi polynomials. One complication is that there are many reasonable measures of optimality as enumerated here. Another is that there are at least three exceptions to the general principle that Chebyshev polynomials give the fastest rate of convergence from the larger family of Jacobi polynomials. When f (x) is singular...

The mathematical theory of closed form functions for calculating LSFs on the basis of generating functions is presented. Exploiting recurrence relationships in the series expansion of Chebyshev polynomials of the first kind makes it possible to bootstrap iterative LSF-search from a set of characteristic polynomial zeros. The theoretical analysis is based on decomposition of sequences into symme...

In this work, the definition of first and second types multiplicative Chebyshev differential equations is given solutions these are investigated with help power series. Also, properties type polynomials proved. Finally, studies supported numerical examples.

The Chebyshev polynomials have many beautiful properties and countless applications, arising in a variety of continuous settings. They are a sequence of orthogonal polynomials appearing in approximation theory, numerical integration, and differential equations. In this paper we approach them instead as discrete objects, counting the sum of weighted tilings. Using this combinatorial approach, on...

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. r 2003 Elsevier Science (USA). All rights reserved.