@article{16cde738f92049d3b176d89fc591db23,
title = "Spectral methods for pantograph-type differential and integral equations with multiple delays",
abstract = "We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.",
keywords = "Convergence analysis, Delay differential equation, Legendre spectral method, Multiple vanishing delays, Volterra functional integral equation",
author = "Ishtiaq Ali and Hermann BRUNNER and Tao TANG",
note = "Funding Information: Acknowledgements The research of Ali and Tang was supported in part by the Hong Kong Research Grants Council and Hong Kong Baptist University. The research of Brunner was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant No. 9406) and Hong Kong Research Grants Council{\textquoteright}s CERG Grant (CERG HKBU 200207). Tang{\textquoteright}s research was also supported by a Joint Research Fund for Hong Kong and Macau Young Scholars awarded by the National Natural Science Foundarion of China.",
year = "2009",
month = mar,
doi = "10.1007/s11464-009-0010-z",
language = "English",
volume = "4",
pages = "49--61",
journal = "Frontiers of Mathematics in China",
issn = "1673-3452",
publisher = "Higher Education Press",
number = "1",
}