Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
曹外香 副教授, 北京师范大学
Inviter:
洪佳林
Title:
A class of efficient spectral methods and error analysis for nonlinear Hamiltonian systems
Time & Venue:
2018.8.31 14:30-15:30 N222
Abstract:
In this talk，we will present andstudy efficient numerical methods for nonlinear Hamiltonian systems, where three kinds of spectral methods (including spectral Petrov-Galerkin, spectral collocation and spectral Galerkin methods) are presented andanalyzed. Our main results include the energy and symplectic structure preserving properties and error estimates of the three spectral methods. We prove that the Petrov-Galerkin method preserves the energy exactly while both Gauss collocation and spectral Galerkin methods are energy conserving up to a spectral accuracy. By the investigation of the difference among the three numerical methods, we also prove that the Petrov Galerkin method and the spectral Galerkin method separately preserves the symplectic structure up to a Gauss numerical quadrature error and a spectral accuracy error. Finally, we show that all the three spectral methods converge exponentially, which makes it possible to simulate the long time behavior. Numerical experiments indicate that our algorithms are efficient.