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

Kun Jiang ,  Qiumei Huang and Xiuxiu Xu

10.4208/aamm.OA-2019-0116

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

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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.

  • History

Published online: 2019-12

  • AMS Subject Headings

65L60, 65L70

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