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
Lecturer
Date
22nd April ~ 12th July, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Thursday | 09:15 - 11:55 | A3-1-103 | ZOOM 2 | 638 227 8222 | BIMSA |
Reference
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.
Video Public
Yes
Notes Public
Yes
Language
Chinese
Lecturer Intro
Zaijiu Shang is a Professor of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and a Post Teacher at the University of Chinese Academy of Sciences (2015-). He was the deputy director (2003-2011) and the director (2012-2016) of the Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He has been served as a member of editorial boards of Acta Math. Appl. Sinica (2007-), Acta Math. Sinica (2009-), Science China: Mathematics (2013-), and Applied Mathematics (HUST 2013-). He is working in the fields of dynamical systems and geometrical numerical methods. He won the second prize in “the Science and Technology Progress Award of the State Education Commission (1993)”. He was one of the core members of the project “Symplectic Geometric Algorithms of Hamiltonian Systems” which won the first prize of the National Natural Science Awards (Kang Feng etc., 1997), and his representative achievements include stability theory of symplectic algorithms and volume-preserving algorithms for source-free systems.