Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations

Authors

  • Kun Jiang College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Qiumei Huang College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Xiuxiu Xu School of Mathematical Sciences, Anhui University, Hefei 230031, China

DOI:

https://doi.org/10.4208/aamm.OA-2019-0116

Keywords:

Multi-pantograph, discontinuous Galerkin method, global convergence, local superconvergence, weakly singular, graded meshes.

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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Published

2020-03-06

Issue

Vol. 12 No. 1 (2020)

Section

Articles