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A New Jacobi Rational-Gauss Collocation Method For Numerical Solution of Generalized Pantograph Equations

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Date

2014

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Elsevier

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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. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.

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Functional Differential Equations, Pantograph Equation, Collocation Method, Jacobi Rational-Gauss Quadrature, Jacobi Rational Function

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Source

Applied Numerical Mathematics

Volume

77

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Start Page

43

End Page

54