报告题目：Long-term analysis of symmetric and/or symplectic extended RKN integrators
报 告 人：吴新元 曲阜师范大学特聘教授、南京大学教授
时 间：2019年6月21号 下午 16:00-16:50
报告摘要: The primary objective of this talk is to present a long-term numerical energy-preserving analysis of one-stage explicit symmetric and/or symplectic extended Runge-Kutta-Nystrom (ERKN) integrators for highly oscillatory Hamiltonian systems. We study the long-time numerical energy conservation not only for symmetric integrators but also for symplectic integrators. It turns out that these both kinds of ERKN integrators have a near conservation of the total and oscillatory energy over a long term. Moreover, this talk also analyses the long-time behaviour of ERKN integrators when applied to nonlinear wave equations. It is shown that energy, momentum, and all harmonic actions are approximately preserved over a long time for one-stage explicit symplectic or symmetric ERKN integrators when applied to nonlinear wave equations via spectral semi-discretisations.