Geometric numerical integration
This course is an introduction to geometric numerical integration for ordinary differential equations based on the theory of dynamical systems. The course will cover the following topics:
1) Brief introduction to basics of dynamical systems;
2) K. Feng’s idea on geometric numerical integration;
3) Symplectic integration methods for Hamiltonian systems;
4) Backward error theory of geometric integration methods;
5) Linear stability of symplectic methods;
6) Nonlinear stability of symplectic methods
1) Brief introduction to basics of dynamical systems;
2) K. Feng’s idea on geometric numerical integration;
3) Symplectic integration methods for Hamiltonian systems;
4) Backward error theory of geometric integration methods;
5) Linear stability of symplectic methods;
6) Nonlinear stability of symplectic methods
讲师
日期
2023年04月03日 至 07月10日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一 | 09:00 - 11:25 | A3-1-101 | ZOOM 05 | 293 812 9202 | BIMSA |
参考资料
1. V. I. Arnold, Mathematical Methods of Classical Mechanics (Appendix 1-8 and relevant references up to date), Springer-Verlag New York, 1978.
2. S. Blanes and F. Casas, A Concise Introduction to Geometric Numerical Integration, CRC Press Taylor & Francis Group Boca Raton 2016.
3. K. Feng and M. Z. Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Zhejiang Science and Technology Press Hangzhou and Springer-Verlag Berlin, 2010.
4. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration ---Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag Berlin, 2nd edit. 2006.
5. A. M. Stuart and A. R. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, 1996.
2. S. Blanes and F. Casas, A Concise Introduction to Geometric Numerical Integration, CRC Press Taylor & Francis Group Boca Raton 2016.
3. K. Feng and M. Z. Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Zhejiang Science and Technology Press Hangzhou and Springer-Verlag Berlin, 2010.
4. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration ---Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag Berlin, 2nd edit. 2006.
5. A. M. Stuart and A. R. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, 1996.
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
尚在久，中国科学院数学与系统科学研究院研究员、博士生导师，中国科学院大学岗位教师。曾任中国科学院数学与系统科学研究院数学研究所副所长（2003-2011）、所长（2012-2016）。 《中国科学：数学》（中、英文版）、 《数学学报》（中、英文版）、 《应用数学学报》（中、英文版）、《应用数学》（华中科技大学）等期刊编委。
从事动力系统与几何数值方法的研究，曾获国家教委科技进步二等奖（1993），是国家自然科学一等奖获奖项目“哈密尔顿系统的辛几何算法“（冯康等，1997）的主要骨干成员，代表性成果有“辛算法的稳定性理论”、“保体积算法”等。