The symplectic numerical methods preserve the symplectic property of phase flow of Hamiltonian systems, and play a very important role in scientific computation. In this talk we review some results on the construction, numerical analysis and applications of symplectic numerical methods for Hamiltonian systems, inclusive of deterministic and stochastic cases.

洪佳林：中国科学院数学与系统科学研究院研究员、博士生导师、副院长。