Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type

Hermann Brunner; Qiumei Huang; Hehu Xie

doi:10.1137/090771922

Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type

Hermann Brunner^*
, Qiumei Huang
, Hehu Xie

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

86 Citations (Scopus)

29 Downloads (Pure)

Abstract

This paper is concerned with the application of the discontinuous Galerkin method to delay differential equations with vanishing delay qt (0 < q < 1). Our aim is to establish optimal global and local superconvergence results on uniform meshes and compare these with analogous estimates for collocation methods. The theoretical results are illustrated by a broad range of numerical examples.

Original language	English
Pages (from-to)	1944-1967
Number of pages	24
Journal	SIAM Journal on Numerical Analysis
Volume	48
Issue number	5
DOIs	https://doi.org/10.1137/090771922
Publication status	Published - 30 Nov 2010

User-Defined Keywords

Discontinuous Galerkin method
Optimal order of superconvergence
Pantograph delay differential equations
Vanishing proportional delay

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title = "Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type",

abstract = "This paper is concerned with the application of the discontinuous Galerkin method to delay differential equations with vanishing delay qt (0 < q < 1). Our aim is to establish optimal global and local superconvergence results on uniform meshes and compare these with analogous estimates for collocation methods. The theoretical results are illustrated by a broad range of numerical examples.",

keywords = "Discontinuous Galerkin method, Optimal order of superconvergence, Pantograph delay differential equations, Vanishing proportional delay",

author = "Hermann Brunner and Qiumei Huang and Hehu Xie",

note = "Funding information: Department of Mathematics \& Statistics, Memorial Univers ity of Newfoundland, St. John{\textquoteright}s, NL, A1C 5S7, Canada, and Department of Mathematics, Hong Kong Baptist University, Hong Kong, China ([email protected]). This author{\textquoteright}s research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery grant 9406). §LSEC, ICMSEC, Academy of Mathematics and Systems Sc ience, Chinese Academy of Sciences, Beijing 100190, China ([email protected]). This author{\textquoteright}s research was supported in part by the Natural Science Foundation of China (NSFC 11001259). Publisher copyright: Copyright {\textcopyright} 2010 Society for Industrial and Applied Mathematics",

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doi = "10.1137/090771922",

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AU - Huang, Qiumei

AU - Xie, Hehu

N1 - Funding information: Department of Mathematics & Statistics, Memorial Univers ity of Newfoundland, St. John’s, NL, A1C 5S7, Canada, and Department of Mathematics, Hong Kong Baptist University, Hong Kong, China ([email protected]). This author’s research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery grant 9406). §LSEC, ICMSEC, Academy of Mathematics and Systems Sc ience, Chinese Academy of Sciences, Beijing 100190, China ([email protected]). This author’s research was supported in part by the Natural Science Foundation of China (NSFC 11001259). Publisher copyright: Copyright © 2010 Society for Industrial and Applied Mathematics

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N2 - This paper is concerned with the application of the discontinuous Galerkin method to delay differential equations with vanishing delay qt (0 < q < 1). Our aim is to establish optimal global and local superconvergence results on uniform meshes and compare these with analogous estimates for collocation methods. The theoretical results are illustrated by a broad range of numerical examples.

AB - This paper is concerned with the application of the discontinuous Galerkin method to delay differential equations with vanishing delay qt (0 < q < 1). Our aim is to establish optimal global and local superconvergence results on uniform meshes and compare these with analogous estimates for collocation methods. The theoretical results are illustrated by a broad range of numerical examples.

KW - Discontinuous Galerkin method

KW - Optimal order of superconvergence

KW - Pantograph delay differential equations

KW - Vanishing proportional delay

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DO - 10.1137/090771922

M3 - Journal article

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EP - 1967

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 5

ER -

Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type

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