In this study, we suggest an efficient and useful method by using Chebyshev polynomials to approximate eigenvalues of a non-singular sixth-order Sturm-Liouville equation. This method uses Chebyshev polynomials and integration operation matrix for approximating of function and its derivatives. We convert the original problem for finding the eigenvalues of Sturm-Liouville problem to a problem of ...

In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order Ds = ( √ 1− x2∂x) is developed for nonlinear conservation laws. The boundary conditions are treated by a penalty method. Compared with the second-order spectral viscosity method, the super one is much weaker while still guaranteeing the convergence of the bounded solution of the Chebyshev–Ga...

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...

4 Some specific cutting-plane methods 12 4.1 Bisection method on R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Center of gravity method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.3 MVE cutting-plane method . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.4 Chebyshev center cutting-plane method . . . . . . . . . . . . . . . . . . . . . 16 4.5 ...

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...

In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the subspace method for computing eigenvalues with largest real parts and corresponding eigenvectors non-symmetric matrices. As by-products, generalizations Chebyshev–Davidson solving eigenvalue problems are also presented. We give convergence analysis complex Chebyshev polynomial, which plays significant rol...

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...