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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: 教授 (曲阜师范大学)

  目:Long-term analysis of symmetric and/or symplectic extended RKN integrators

  间:2019.04.24(星期三), 16 :30-17:30

  点:数学院南楼N913

  

 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.

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