Abstract
In this article, a spectral collocation method based on the Chebyshev polynomials is investigated for the approximate solution of a class of neutral functional-differential equations with variable coefficients, which have many applications in mathematical physics. A Chebyshev collocation method based on Chebyshev Gauss-Lobatto quadrature points is utilized to reduce the solution of such problem to a system of algebraic equations. In addition, accurate approximation is obtained by selecting few Chebyshev Gauss-Lobatto collocation points. Comparing the numerical results with those of known techniques shows that the present method is better in terms of accuracy over the other methods mentioned in this paper.