@article{0da93416d7d841d88df57fce1ecb744d,
title = "Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type",
abstract = "This paper is concerned with the application of the discontinuous Galerkin method to delay differential equations with vanishing delay qt (0 < q < 1). Our aim is to establish optimal global and local superconvergence results on uniform meshes and compare these with analogous estimates for collocation methods. The theoretical results are illustrated by a broad range of numerical examples.",
keywords = "Discontinuous Galerkin method, Optimal order of superconvergence, Pantograph delay differential equations, Vanishing proportional delay",
author = "Hermann Brunner and Qiumei Huang and Hehu Xie",
note = "Funding information: Department of Mathematics & Statistics, Memorial Univers ity of Newfoundland, St. John{\textquoteright}s, NL, A1C 5S7, Canada, and Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (hbrunner@math.hkbu.edu.hk). This author{\textquoteright}s research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery grant 9406). §LSEC, ICMSEC, Academy of Mathematics and Systems Sc ience, Chinese Academy of Sciences, Beijing 100190, China (hhxie@lsec.cc.ac.cn). This author{\textquoteright}s research was supported in part by the Natural Science Foundation of China (NSFC 11001259). Publisher copyright: Copyright {\textcopyright} 2010 Society for Industrial and Applied Mathematics",
year = "2010",
month = nov,
day = "30",
doi = "10.1137/090771922",
language = "English",
volume = "48",
pages = "1944--1967",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "5",
}