Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations  

作　　者：Kun Jiang Qiumei Huang Xiuxiu Xu 

机构地区：[1]College of Applied Sciences,Beijing University of Technology,Beijing 100124,China [2]School of Mathematical Sciences,Anhui University,Hefei 230031,China

出　　处：《Advances in Applied Mathematics and Mechanics》2020年第1期189-211,共23页应用数学与力学进展（英文）

基　　金：supported by the Natural Science Foundation of China(No.11571027),the International Research Cooperation Seed of Beijing University of Technology(No.2018B32);Science and Technology Projects of Beijing Education Commission Foundatio(No.KM201510005032),and the 16th graduate science and technology fund of Beijing university of technology(No.ykj-2017-00127).

摘　　要：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.

关 键 词：Multi-pantograph discontinuous Galerkin method global convergence local superconvergence weakly singular graded meshes 

分 类 号：O17[理学—数学]