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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...
There exists a strong connection between numerical methods for the integration of ordinary differential equations and optimization problems. In this paper, we try to discover further their links. And ...
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...
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...
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...