TY - JOUR
T1 - Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type
AU - Xu , Xiuxiu
AU - Huang , Qiumei
AU - Chen , Hongtao
JO - Journal of Computational Mathematics
VL - 2
SP - 186
EP - 199
PY - 2016
DA - 2016/04
SN - 34
DO - http://doi.org/10.4208/jcm.1511-m2014-0216
UR - https://global-sci.org/intro/article_detail/jcm/9790.html
KW - Pantograph delay differential equations, Uniform mesh, Continuous Galerkin
methods, Supercloseness, Superconvergence.
AB - <p style="text-align: justify;">This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution $U$ and the interpolation $Π_hu$ of the exact solution $u$. The theoretical results are illustrated by numerical examples.</p>