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

地    点：金沙集团wwW3354CC三楼报告厅304

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.

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