Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations

Discontinuous Galerkin Methods  for  Multi-Pantograph Delay Differential Equations

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.

Author Details

Kun Jiang

Qiumei Huang

Xiuxiu Xu

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