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Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type

Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type
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Year:    2016

Author:    Xiuxiu Xu, Qiumei Huang, Hongtao Chen

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1511-m2014-0216

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 2 : pp. 186–199

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

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

Author Details

Xiuxiu Xu

Qiumei Huang

Hongtao Chen

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