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 uni...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.展开更多
基金Acknowledgments. The second author is supported by NSFC （Nos. 11571027, 91430215）, by Beijing Nova Program （No. 2151100003150140） and by the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions （No. CIT＆TCD201504012）. The third author is supported by the Natural Science Foundation of Fujian Province of China （No.2013J05015）, by NSFC （No.11301437）, and by the Fundamental Research ~nds for the Central Universities （No. 20720150004）.
文摘这份报纸涉及缩放仪的微分方程打的延期的连续 Galerkin 解决方案的 superconvergent 点。我们在一致网孔下面证明本地人是连续 Galerkin 答案的节的 superconvergence 并且基于在连续 Galerkin 答案 U 和准确答案 u 的插值 hu 之间的 supercloseness 定位所有 superconvergent 点。理论结果被数字例子说明。 '
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).
文摘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.
