A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations

Authors:
E. H. Doha;A. H. Bhrawy;D. Baleanu;R. M. Hafez
Affiliations:
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt;Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia and Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt;Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia and Institute of Space Sciences, Magurele-Bucharest, Romania and Dep ...;Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo 11931, Egypt
Venue:
Applied Numerical Mathematics
Year:
2014

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Abstract

This 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.