Bhrawy, A. H.Doha, E. H.Baleanu, D.Hafez, R. M.2019-11-092019-11-0920140168-9274https://www.sciencedirect.com/science/article/abs/pii/S0168927413001530Accession Number: WOS:000329957600004his paper is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this article, a new spectral collocation method is applied to solve the generalized pantograph equation with variable coefficients on a semi-infinite domain. This method is based on Jacobi rational functions and Gauss quadrature integration. The Jacobi rational-Gauss method reduces solving the generalized pantograph equation to a system of algebraic equations. Reasonable numerical results are obtained by selecting few Jacobi rational-Gauss collocation points. The proposed Jacobi rational-Gauss method is favorably compared with other methods. Numerical results demonstrate its accuracy, efficiency, and versatility on the half-line. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.enUniversity for unctional differential equationsPantograph equationCollocation methodJacobi rational-Gauss quadratureJacobi rational functionArticle