TY - JOUR
T1 - Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type
AU - Brunner, Hermann
AU - Huang, Qiumei
AU - Xie, Hehu
N1 - Funding information:
Department of Mathematics & Statistics, Memorial Univers ity of Newfoundland, St. John’s, NL, A1C 5S7, Canada, and Department of Mathematics, Hong Kong Baptist University, Hong Kong, China ([email protected]). This author’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 ([email protected]). This author’s research was supported in part by the Natural Science Foundation of China (NSFC 11001259).
Publisher copyright:
Copyright © 2010 Society for Industrial and Applied Mathematics
PY - 2010/11/30
Y1 - 2010/11/30
N2 - 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.
AB - 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.
KW - Discontinuous Galerkin method
KW - Optimal order of superconvergence
KW - Pantograph delay differential equations
KW - Vanishing proportional delay
UR - http://www.scopus.com/inward/record.url?scp=78649980140&partnerID=8YFLogxK
U2 - 10.1137/090771922
DO - 10.1137/090771922
M3 - Journal article
AN - SCOPUS:78649980140
SN - 0036-1429
VL - 48
SP - 1944
EP - 1967
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 5
ER -