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Quadratic Invariants and Multi-symplecticity of Partitioned Runge-Kutta Methods for Hamiltonian PDEs
Quadratic conservation law Partitioned Runge-Kutta method Multi-symplectic
2012/8/7
In this paper, we study the preservation of quadratic conservation laws of Runge-Kutta
methods and partitioned Runge-Kutta methods for Hamiltonian PDEs and establish the relation
between multi-sympl...
A Note on Symplecticity of Step-Transition Mappings for Multi-Step Methods
Linear multi-step method Infinitesimally symplectic Symplecticity General linear method
2012/8/1
We prove that for a linear multi-step methodm
k=0kZk =m
k=0kf (Zk), even though the mappings Z0 → Z1, . . . , Zm−2 →
Zm−1 are chosen to be symplectic, Zm−1 → Zm will be non-s...
The Multi-Symplecticity of Partitioned Runge-Kutta Methods for Hamiltonian PDEs
Partitioned Runge-Kutta method Multi-symplecticity Hamiltonian partial differential equation
2012/7/31
In this article we consider partitioned Runge-Kutta (PRK) methods for Hamiltonian partial differential equations (PDEs), and present some sufficient conditions for multi-symplecticity of PRK methods o...