报告题目：Long time integration of Hamiltonian systems
报告人：尚在久 研究员 （中国科学院数学与系统科学研究院）
校内联系人：柳振鑫 教授 联系电话：84708351-8039
报告摘要: Very long time integration is needed in many problems described by Hamiltonian systems. For example, simulating stable or chaotic motions of the planets in the solar system and computing trajectory samples in the molecular dynamics are two typical challenging problems of scientific computing. Due to the conservative nature of Hamiltonian systems, most of time integration methods such as the well known Runge-Kutta methods and linear multi-step methods as well as others based on the Lyapunov's stability analysis for dissipation dominated systems are not successful for Hamiltonian systems. Under this background the symplectic numerical approach was systematically proposed in 1980's, which opened a way to tackle long time integration challenges of conservative systems.
In this talk we will give a brief introduction to the symplectic integration and explain to what extent the symplectic integration methods can give a stable numerical simulation to the typical dynamics of Hamiltonian systems. The explanation is mainly based on the stability analysis of Hamiltonian systems and backward analysis of symplectic methods.