Legendre spectral collocation methods for pantograph Volterra delay-integro-differential equations
type: Item
instance of: scholarly article
title: Legendre spectral collocation methods for pantograph Volterra delay-integro-differential equations
zbMATH Open document ID: 1264.65218
author: Yunxia Wei
author: Yanping Chen
published in: Journal of Scientific Computing
publication date: 2013-02-04T00:00:00Z
review text: A Legendre spectral collocation method is proposed for linear pantograph Volterra delay integro-differential equations. The method is based on a basis of Lagrange interpolation polynomials of order \(N\) using Legendre-Gauss points as knots and on the Gauss quadrature formula. The main contribution of this paper is the convergence analysis providing that the errors of the approximate solution and approximate first order derivative decay exponentially in \(L^2\)-norm and \(L_\infty\)-norm. Two numerical examples on the interval \([-1,1]\) and \([0,20]\), respectively, are presented in order to illustrate the effectiveness and the performances of the method showing the exponential decay of the errors plotted for \(1<N<17\) both for the approximate solution and for its first derivative.
reviewed by: Alexandru Mihai Bica
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45A05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 6134430
zbMATH Keywords: Volterra delay integro-differential equations
zbMATH Keywords: Gauss quadrature formula
zbMATH Keywords: convergence
zbMATH Keywords: Legendre spectral collocation method
zbMATH Keywords: linear pantograph Volterra delay integro-differential equations
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: s10915-012-9595-6
OpenAlex ID: W2083183137
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DOI: 10.1007/S10915-012-9595-6
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description: scientific article; zbMATH DE number 6134430