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...

The spectral collocation method for solving two-point boundary value problems second order differential equations is implemented, based on representing the solution as an expansion in Chebyshev polynomials. approach allows a stable calculation of both representation and its pointwise any required grid definition domain equation additional conditions multipoint problem. For effective constructio...

In this paper, numerical solution of linear Fredholm integral equations of the second kind is considered by two methods. The methods are developed by means of the Sinc-collocation method and shifted Chebyshev polynomial method. Some numerical examples are presented to illustrate the method. Numerical solution of linear Fredholm integral equations. 1. Introduction Many initial and boundary value...

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...