Superconvergence of Discontinuous Galerkin Solutions for Delay Differential Equations of Pantograph Type

Qiumei Huang; Hehu Xie; Hermann Brunner

doi:10.1137/110824632

Superconvergence of Discontinuous Galerkin Solutions for Delay Differential Equations of Pantograph Type

SIAM Journal on Scientific Computing ◽

10.1137/110824632 ◽

2011 ◽

Vol 33 (5) ◽

pp. 2664-2684 ◽

Cited By ~ 8

Author(s):

Qiumei Huang ◽

Hehu Xie ◽

Hermann Brunner

Keyword(s):

Differential Equations ◽

Discontinuous Galerkin ◽

Delay Differential Equations ◽

Delay Differential

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Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type

SIAM Journal on Numerical Analysis ◽

10.1137/090771922 ◽

2010 ◽

Vol 48 (5) ◽

pp. 1944-1967 ◽

Cited By ~ 32

Author(s):

Hermann Brunner ◽

Qiumei Huang ◽

Hehu Xie

Keyword(s):

Differential Equations ◽

Discontinuous Galerkin ◽

Delay Differential Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Delay Differential

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Superconvergence of discontinuous Galerkin methods for nonlinear delay differential equations with vanishing delay

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.08.029 ◽

2019 ◽

Vol 348 ◽

pp. 314-327 ◽

Cited By ~ 1

Author(s):

Xiuxiu Xu ◽

Qiumei Huang

Keyword(s):

Differential Equations ◽

Discontinuous Galerkin ◽

Delay Differential Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Nonlinear Delay Differential Equations ◽

Vanishing Delay ◽

Delay Differential ◽

Nonlinear Delay

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Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.oa-2019-0116 ◽

2020 ◽

Vol 12 (1) ◽

pp. 189-211

Author(s):

Kun Jiang

Keyword(s):

Differential Equations ◽

Discontinuous Galerkin ◽

Delay Differential Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Delay Differential

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Nonlinear stability of discontinuous Galerkin methods for delay differential equations

Applied Mathematics Letters ◽

10.1016/j.aml.2009.12.003 ◽

2010 ◽

Vol 23 (4) ◽

pp. 457-461 ◽

Cited By ~ 17

Author(s):

Dongfang Li ◽

Chengjian Zhang

Keyword(s):

Differential Equations ◽

Discontinuous Galerkin ◽

Nonlinear Stability ◽

Delay Differential Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Delay Differential

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The $hp$ Discontinuous Galerkin Method for Delay Differential Equations with Nonlinear Vanishing Delay

SIAM Journal on Scientific Computing ◽

10.1137/120901416 ◽

2013 ◽

Vol 35 (3) ◽

pp. A1604-A1620 ◽

Cited By ~ 9

Author(s):

Qiumei Huang ◽

Hehu Xie ◽

Hermann Brunner

Keyword(s):

Differential Equations ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Delay Differential Equations ◽

Vanishing Delay ◽

Delay Differential

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An hp-version of the discontinuous Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2019.112348 ◽

2020 ◽

Vol 364 ◽

pp. 112348

Author(s):

Yichen Wei ◽

Tao Sun ◽

Lijun Yi

Keyword(s):

Differential Equations ◽

Discontinuous Galerkin ◽

Delay Differential Equations ◽

Second Order ◽

Time Stepping ◽

Delay Differential

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Numerical Solutions of Nonautonomous Stochastic Delay Differential Equations by Discontinuous Galerkin Methods

Journal of Computational Mathematics ◽

10.4208/jcm.1806-m2017-0296 ◽

2019 ◽

Vol 37 (3) ◽

pp. 419-436

Author(s):

Xinjie Dai and Aiguo Xiao

Keyword(s):

Differential Equations ◽

Discontinuous Galerkin ◽

Delay Differential Equations ◽

Discontinuous Galerkin Methods ◽

Numerical Solutions ◽

Galerkin Methods ◽

Stochastic Delay Differential Equations ◽

Stochastic Delay ◽

Delay Differential

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Superconvergence of discontinuous Galerkin method for neutral delay differential equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2020.1846030 ◽

2020 ◽

pp. 1-15

Author(s):

Gengen Zhang ◽

Xinjie Dai

Keyword(s):

Differential Equations ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Delay Differential Equations ◽

Neutral Delay ◽

Neutral Delay Differential Equations ◽

Delay Differential

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On discontinuous Galerkin finite element method for singularly perturbed delay differential equations

Applied Mathematics Letters ◽

10.1016/j.aml.2014.06.013 ◽

2014 ◽

Vol 38 ◽

pp. 27-32 ◽

Cited By ~ 15

Author(s):

Helena Zarin

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Differential Equations ◽

Discontinuous Galerkin ◽

Delay Differential Equations ◽

Singularly Perturbed ◽

Galerkin Finite Element Method ◽

Galerkin Finite Element ◽

Discontinuous Galerkin Finite Element ◽

Delay Differential

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error estimates of discontinuous Galerkin methods for delay differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2014.01.008 ◽

2014 ◽

Vol 82 ◽

pp. 1-10 ◽

Cited By ~ 23

Author(s):

Dongfang Li ◽

Chengjian Zhang

Keyword(s):

Differential Equations ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Delay Differential Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Delay Differential

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