Bhrawy, A. H.Baleanu, D.Hafez, R. M.Doha, E. H.2020-05-032025-09-182020-05-032025-09-1820140168-92741873-5460https://doi.org/10.1016/j.apnum.2013.11.003https://hdl.handle.net/20.500.12416/14775Doha, Eid/0000-0002-7781-6871; Hafez, Ramy/0000-0001-9533-3171This 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 FunctionArticle10.1016/j.apnum.2013.11.0032-s2.0-84888631283