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

Qiumei Huang; Hehu Xie; Hermann Brunner

doi:10.1137/120901416

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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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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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 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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Local discontinuous Galerkin method for time variable order fractional differential equations with sub-diffusion and super-diffusion

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.07.015 ◽

2020 ◽

Vol 157 ◽

pp. 602-618

Author(s):

M. Ahmadinia ◽

Z. Safari ◽

M. Abbasi

Keyword(s):

Differential Equations ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Fractional Differential Equations ◽

Local Discontinuous Galerkin Method ◽

Time Variable ◽

Variable Order ◽

Local Discontinuous Galerkin ◽

Fractional Differential

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Stability analysis of discontinuous Galerkin method for stiff Volterra functional differential equations

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2019.03.013 ◽

2019 ◽

Vol 475 (2) ◽

pp. 1293-1303 ◽

Cited By ~ 1

Author(s):

Gengen Zhang ◽

Guoman He ◽

Xinjie Dai

Keyword(s):

Stability Analysis ◽

Differential Equations ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Functional Differential Equations ◽

Functional Differential

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Interpolating Runge-Kutta methods for vanishing delay differential equations

Computing ◽

10.1007/bf02238433 ◽

1995 ◽

Vol 55 (3) ◽

pp. 223-236 ◽

Cited By ~ 7

Author(s):

W. H. Enright ◽

M. Hu

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Runge Kutta ◽

Vanishing Delay ◽

Delay Differential

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Analysis of a posteriori error estimates of the discontinuous Galerkin method for nonlinear ordinary differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2016.03.008 ◽

2016 ◽

Vol 106 ◽

pp. 129-153 ◽

Cited By ~ 11

Author(s):

Mahboub Baccouch

Keyword(s):

Differential Equations ◽

Galerkin Method ◽

Ordinary Differential Equations ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Nonlinear Ordinary Differential Equations ◽

A Posteriori ◽

A Posteriori Error

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Characteristic Orthogonal Polynomial based Galerkin Method for Solving Fractional Order Delay Differential Equations

Communications in Numerical Analysis ◽

10.5899/2019/cna-00387 ◽

2019 ◽

Vol 2019 (2) ◽

pp. 91-101

Author(s):

Rajarama Mohan Jena ◽

S. Chakraverty

Keyword(s):

Differential Equations ◽

Galerkin Method ◽

Orthogonal Polynomial ◽

Fractional Order ◽

Delay Differential Equations ◽

Delay Differential

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An adaptive discontinuous Galerkin method for very stiff systems of ordinary differential equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.04.011 ◽

2019 ◽

Vol 358 ◽

pp. 330-347

Author(s):

A. Fortin ◽

D. Yakoubi

Keyword(s):

Differential Equations ◽

Galerkin Method ◽

Ordinary Differential Equations ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Stiff Systems

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A discontinuous Galerkin method for systems of stochastic differential equations with applications to population biology, finance, and physics

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113297 ◽

2021 ◽

Vol 388 ◽

pp. 113297

Author(s):

Mahboub Baccouch ◽

Helmi Temimi ◽

Mohamed Ben-Romdhane

Keyword(s):

Differential Equations ◽

Galerkin Method ◽

Stochastic Differential Equations ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Population Biology

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