Doha, E. H.Bhrawy, A. H.Baleanu, DumitruHafez, R. M.2020-05-032020-05-0320140168-92741873-5460http://hdl.handle.net/20.500.12416/3599This 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.eninfo:eu-repo/semantics/closedAccessFunctional Differential EquationsPantograph EquationCollocation MethodJacobi Rational-Gauss QuadratureJacobi Rational FunctionArticle77435410.1016/j.apnum.2013.11.003