学术报告

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）

报告时间：2017年7月14日（星期五）下午15:00-16:00

报告地点：创新园大厦 A1101

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.

报告人简介：尚在久老师现为中国科学院数学与系统科学研究院研究员，数学研究所所长。主要从事Hamilton系统的研究。