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 - <p style="text-align: justify;">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.</p>