Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary differential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the o...

Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1 + x) and 1/(x − a) where a > 1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this.  2005 IMACS. Published by...

In this paper we study convergence and computation of interpolatory quadrature formulas with respect to a wide variety of weight functions. The main goal is to evaluate accurately a definite integral, whose mass is highly concentrated near some points. The numerical implementation of this approach is based on the calculation of Chebyshev series and some integration formulas which are exact for ...

In this paper we propose, a collocation method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semiinfnite interval. This approach is based on generalized Laguerre polynomials and rational Chebyshev functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with...

This thesis is based on the following paper :Mehdi Dehghan , M.R. Eslahchi, Best uniform polynomialapproximation of some rational functions , Computers andMathematics with Applications ,Best polynomial approximation problem is one of the mostimportant and applicable subjects in the approxi References1. [1] J . C . Mason , D . C . Handscomb , Chebyshevpolynomials ...

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...