Volume 12, Issue 1
Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations

Adv. Appl. Math. Mech., 12 (2020), pp. 189-211.

Published online: 2019-12

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• Abstract

In this paper, the discontinuous Galerkin method is applied to solve the multi-pantograph delay differential equations. We analyze the optimal global convergence and local superconvergence for smooth solutions under uniform meshes. Due to the initial singularity of the forcing term $f$, solutions of multi-pantograph delay differential equations are singular. We obtain the relevant global convergence and local superconvergence for weakly singular solutions under graded meshes. The numerical examples are provided to illustrate our theoretical results.

65L60, 65L70

jkmath@126.com (Kun Jiang)

qmhuang@bjut.edu.cn (Qiumei Huang)

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

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@Article{AAMM-12-189, author = {Jiang , KunHuang , Qiumei and Xu , Xiuxiu}, title = {Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {12}, number = {1}, pages = {189--211}, abstract = {

In this paper, the discontinuous Galerkin method is applied to solve the multi-pantograph delay differential equations. We analyze the optimal global convergence and local superconvergence for smooth solutions under uniform meshes. Due to the initial singularity of the forcing term $f$, solutions of multi-pantograph delay differential equations are singular. We obtain the relevant global convergence and local superconvergence for weakly singular solutions under graded meshes. The numerical examples are provided to illustrate our theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0116}, url = {http://global-sci.org/intro/article_detail/aamm/13424.html} }
TY - JOUR T1 - Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations AU - Jiang , Kun AU - Huang , Qiumei AU - Xu , Xiuxiu JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 189 EP - 211 PY - 2019 DA - 2019/12 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0116 UR - https://global-sci.org/intro/article_detail/aamm/13424.html KW - Multi-pantograph, discontinuous Galerkin method, global convergence, local superconvergence, weakly singular, graded meshes. AB -

In this paper, the discontinuous Galerkin method is applied to solve the multi-pantograph delay differential equations. We analyze the optimal global convergence and local superconvergence for smooth solutions under uniform meshes. Due to the initial singularity of the forcing term $f$, solutions of multi-pantograph delay differential equations are singular. We obtain the relevant global convergence and local superconvergence for weakly singular solutions under graded meshes. The numerical examples are provided to illustrate our theoretical results.

Kun Jiang, Qiumei Huang & Xiuxiu Xu. (2019). Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations. Advances in Applied Mathematics and Mechanics. 12 (1). 189-211. doi:10.4208/aamm.OA-2019-0116
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