| 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. |
| 关键词: 谱配置法 初值问题 超收敛 |
| DOI：10.3969/J.ISSN.1000-5137.2021.01.001 |
| 分类号:O241.8 |
| 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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| 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, YI Lijun
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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. |
| Key words: spectral collocation method initial value problem superconvergence |
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