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GALERKIN AND RUNGE{KUTTA METHODS: UNIFIED FORMULATION, A POSTERIORI ERROR ESTIMATES AND NODAL SUPERCONVERGENCE
Continuous discontinuous Galerkin methods
2015/12/11
We unify the formulation and analysis of Galerkin and Runge{Kutta
methods for the time discretization of parabolic equations. This, together with
the concept of reconstruction of the approximate sol...
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...
ASYMPTOTIC BEHAVIOR OF MULTISTEP RUNGE-KUTTA METHODS FOR SYSTEMS OF DELAY DIFFERENTIAL EQUATIONS
Stability multistep Runges-Ku
2007/12/10
This paper deals with the asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations (DDEs). With the help of K.J.in't Hout's analytic technique for the numerical...
Equilibrium Attractive Properties of A Class of Multistep Runge-Kutta Methods
Initial value problems Ordinary differential equations Multistep Runge–Kutta methods Equilibrium attractivity
2012/8/1
The main purpose of this paper is to discuss the equilibrium attractive properties of a class of multistep Runge–Kutta methods for initial value problems of ordinary differential equations. Some algeb...
Some Properties of Multi-symplectic Runge-Kutta Methods for Nonlinear Dirac Equations
Multi-symplectic RK methods Conservation Laws Nonliear Dirac Equations
2012/7/31
In this paper, we investigate some properties of the multi-symplectic Runge-Kutta (MSRK) methods for nonlinear Dirac equations in relativistic quantum physics. It is showed that the symplectic Runge-K...
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...