文章基本信息

标题：A Legendre-Gauss collocation method for neutral functional-differential equations with proportional delays
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作者：Ali H Bhrawy ; Laila M Assas ; Emran Tohidi 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：63
DOI：10.1186/1687-1847-2013-63
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we present a unified framework for analyzing the spectral collocation method for neutral functional-differential equations with proportional delays using shifted Legendre polynomials. The proposed collocation technique is based on shifted Legendre-Gauss quadrature nodes as collocation knots. Error analysis and stability of the proposed algorithm are theoretically investigated under several mild conditions. The accuracy of the proposed method has been compared with a variational iteration method, a one-leg θ-method, a particular Runge-Kutta method, and a reproducing kernel Hilbert space method. Numerical results show that the proposed methods are of high accuracy and are efficient for solving such an equation. Also, the results demonstrate that the proposed method is a powerful algorithm for solving other delay differential equations.
关键词：delay differential equations ; neutral functional-differential equations ; proportional delays ; spectral method ; Legendre-Gauss quadrature