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Speaker:
Professor Hong Jialin
(Chinese Academy
of Sciences)
Time:
May 11 (Thurs.), 2006
AM
11.00~12.00
Topic:
Multi-symplectic Runge-Kutta type methods for Hamiltonian
partial differential equations
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Abstract:
Mathematicians and scientists have paid much more attention
to structure-preserving algorithms of dynamical systems since Professor
Kang Feng proposed and systematically developed the so-called symplectic
algorithms for Hamiltonian systems in the late 1980s. Multi-symplectic
numerical methods for infinite–dimensional Hamiltonian systems, such as
Dirac equations and Schroedinger equations, play an important role in
scientific and engineering computing. In this talk, we introduce some
fundamental results on symplectic Runge-Kutta type methods for Hamiltonian
ordinary differential equations, and discuss the multi-symplecticity of
Runge-Kutta type methods, including partitioned Runge-Kutta methods and
Nystroem methods, etc, for Hamiltonian partial differential equations.
We give some explicit multi-symplectic Runge-Kutta type methods for
Hamiltonian wave equations. We present some applications of these methods
to Dirac equations and Schroedinger equations in quantum physics, and
investigate conservative properties of energy and momentum for these
methods.
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