LOCAL SUPERCONVERGENCE OF CONTINUOUS GALERKIN SOLUTIONS FOR DELAY DIFFERENTIAL EQUATIONS OF PANTOGRAPH TYPE
- ISSN号:0254-9409
- 期刊名称:《计算数学:英文版》
- 时间:0
- 分类:O241.83[理学—计算数学;理学—数学] O241.8[理学—计算数学;理学—数学]
- 作者机构:[1]Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China, [2]School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen 361005, China
- 相关基金: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).
关键词:
GALERKIN解, 延迟微分方程, 受电弓, 局部收敛, 超收敛点, 均匀网格, 超逼近, 精确解, Pantograph delay differential equations, Uniform mesh, Continuous Galerkinmethods, Supercloseness, Superconvergence.
中文摘要:
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。 '
英文摘要:
This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.