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Volume 34, Issue 2
Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type

Xiuxiu Xu, Qiumei Huang & Hongtao Chen

DOI: 10.4208/jcm.1511-m2014-0216

J. Comp. Math., 34 (2016), pp. 186-199.

Published online: 2016-04

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  • Abstract

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.

  • Keywords

Pantograph delay differential equations, Uniform mesh, Continuous Galerkin methods, Supercloseness, Superconvergence.

  • AMS Subject Headings

65L60, 65N70.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xuxiuxiu@emails.bjut.edu.cn (Xiuxiu Xu)

qmhuang@bjut.edu.cn (Qiumei Huang)

chenht@xmu.edu.cn (Hongtao Chen)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-186, author = {Xu , XiuxiuHuang , Qiumei and Chen , Hongtao}, title = {Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {2}, pages = {186--199}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1511-m2014-0216}, url = {http://global-sci.org/intro/article_detail/jcm/9790.html} }
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 -

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.

Xu , XiuxiuHuang , Qiumei and Chen , Hongtao. (2016). Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type. Journal of Computational Mathematics. 34 (2). 186-199. doi:10.4208/jcm.1511-m2014-0216
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