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 classical mechanics
2) Brief introduction to basics of dynamical systems;
3) K. Feng’s idea on geometric numerical integration;
4) Symplectic integration methods for Hamiltonian systems;
5) Backward error theory of geometric integration methods;
6) Linear stability of symplectic methods;
7) Nonlinear stability of symplectic methods
1) Brief introduction to classical mechanics
2) Brief introduction to basics of dynamical systems;
3) K. Feng’s idea on geometric numerical integration;
4) Symplectic integration methods for Hamiltonian systems;
5) Backward error theory of geometric integration methods;
6) Linear stability of symplectic methods;
7) Nonlinear stability of symplectic methods
讲师
日期
2024年04月22日 至 07月12日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周四 | 09:15 - 11:55 | A3-1-103 | ZOOM 2 | 638 227 8222 | BIMSA |
参考资料
1. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag New York, 1978.
2. S. Blanes and F. Casas, A Concise Introduction to Geometric Numerical Integration, CRC Press Taylor & Francis Group Boca Raton2016.
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. M. W. Hirsch, S. Smale, R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Elsevier Academic Press 2004.
6. 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 Raton2016.
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. M. W. Hirsch, S. Smale, R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Elsevier Academic Press 2004.
6. A. M. Stuart and A. R. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, 1996.
视频公开
公开
笔记公开
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。