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Volume 16, Issue 5
Postprocessing of Continuous Galerkin Solutions for Delay Differential Equations with Nonlinear Vanishing Delay

Qiumei Huang, Kun Jiang & Xiuxiu Xu

Int. J. Numer. Anal. Mod., 16 (2019), pp. 718-730.

Published online: 2019-08

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  • Abstract

In this paper we propose several postprocessing techniques to accelerate the convergence of the continuous Galerkin solutions for delay differential equations with nonlinear vanishing delay. They are interpolation postprocessings (including integration type, Lagrange type, and polynomial preserving recovery type) and iteration postprocessing. The theoretical expectations are confirmed by numerical experiments.

  • Keywords

Pantograph delay differential equations, quasi-graded mesh, continuous Galerkin methods, postprocessing, global superconvergence.

  • AMS Subject Headings

65L60, 65L70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

qmhuang@bjut.edu.cn (Qiumei Huang)

jiangkun@emails.bjut.edu.cn (Kun Jiang)

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

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-718, author = {Huang , QiumeiJiang , Kun and Xu , Xiuxiu}, title = {Postprocessing of Continuous Galerkin Solutions for Delay Differential Equations with Nonlinear Vanishing Delay}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {5}, pages = {718--730}, abstract = {

In this paper we propose several postprocessing techniques to accelerate the convergence of the continuous Galerkin solutions for delay differential equations with nonlinear vanishing delay. They are interpolation postprocessings (including integration type, Lagrange type, and polynomial preserving recovery type) and iteration postprocessing. The theoretical expectations are confirmed by numerical experiments.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13250.html} }
TY - JOUR T1 - Postprocessing of Continuous Galerkin Solutions for Delay Differential Equations with Nonlinear Vanishing Delay AU - Huang , Qiumei AU - Jiang , Kun AU - Xu , Xiuxiu JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 718 EP - 730 PY - 2019 DA - 2019/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13250.html KW - Pantograph delay differential equations, quasi-graded mesh, continuous Galerkin methods, postprocessing, global superconvergence. AB -

In this paper we propose several postprocessing techniques to accelerate the convergence of the continuous Galerkin solutions for delay differential equations with nonlinear vanishing delay. They are interpolation postprocessings (including integration type, Lagrange type, and polynomial preserving recovery type) and iteration postprocessing. The theoretical expectations are confirmed by numerical experiments.

Huang , QiumeiJiang , Kun and Xu , Xiuxiu. (2019). Postprocessing of Continuous Galerkin Solutions for Delay Differential Equations with Nonlinear Vanishing Delay. International Journal of Numerical Analysis and Modeling. 16 (5). 718-730. doi:
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