中科院数学与系统科学研究院
数学研究所
动力系统研讨班报告
报告人: 王 斌 教授 (曲阜师范大学)
题 目:Long-term analysis of symmetric and/or symplectic extended RKN integrators
时 间:2019.04.24(星期三), 16 :30-17:30
地 点:数学院南楼N913室
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–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.