Year: 2020
Author: Kun Jiang, Qiumei Huang, Xiuxiu Xu
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0116
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 189–211
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Multi-pantograph discontinuous Galerkin method global convergence local superconvergence weakly singular graded meshes.
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