| 谱配置法求解常微分方程初值问题的超收敛性 |
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| 引用本文： | 钱轶昀,查媛媛,蔡康文,刘艳勤,王心怡,易利军.谱配置法求解常微分方程初值问题的超收敛性[J].上海师范大学学报(自然科学版),2021,50(1):1-7. |
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| 作者姓名： | 钱轶昀 查媛媛 蔡康文 刘艳勤 王心怡 易利军 |
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| 作者单位： | 上海师范大学 数理学院, 上海 200234,上海师范大学 数理学院, 上海 200234,上海师范大学 数理学院, 上海 200234,上海师范大学 数理学院, 上海 200234,上海师范大学 数理学院, 上海 200234,上海师范大学 数理学院, 上海 200234 |
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| 基金项目： | 上海师范大学“大学生创新创业训练计划”资助项目 |
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| 摘 要： | 研究了常微分方程初值问题的谱配置方法.针对一阶和二阶线性常微分方程初值问题,基于Legendre-Gauss点提出了相应的谱配置方法,并给出了具体的计算格式.最后,通过一些数值算例探讨了所提Legendre-Gauss谱配置方法的超收敛性.
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| 关 键 词： | 谱配置法 初值问题 超收敛 |
| 收稿时间： | 2020/10/17 0:00:00 |
Superconvergence of spectral collocation method for initial value problem of ordinary differential equations |
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| QIAN Yiyun,ZHA Yuanyuan,CAI Kangwen,LIU Yanqin,WANG Xinyi and YI Lijun.Superconvergence of spectral collocation method for initial value problem of ordinary differential equations[J].Journal of Shanghai Normal University(Natural Sciences),2021,50(1):1-7. |
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| Authors: | QIAN Yiyun ZHA Yuanyuan CAI Kangwen LIU Yanqin WANG Xinyi and YI Lijun |
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| Institution: | Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China,Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China,Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China,Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China,Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China and Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China |
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| Abstract: | In this paper, we study the spectral collocation method for the initial value problems of ordinary differential equations. Based on Legendre-Gauss points, we propose the spectral collocation method for the initial value problems of first-order and second-order. We also give the specific computation form for our method. Finally, to explain the superconvergence properties of the Legendre-Gauss spectral collocation method. We discuss several numerical examples. |
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| Keywords: | spectral collocation method initial value problem superconvergence |
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