Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	王斌教授，曲阜师范大学
Inviter:
Title:	Long-term analysis of symmetric and/or symplectic extended RKN integrators
Time & Venue:	2019.4.24 16:30-17:30 N913
Abstract:	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–Nystr¨om (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 semidiscretisations.