Backward error analysis for multi-symplectic integration methods
نویسندگان
چکیده
منابع مشابه
Backward error analysis for multi-symplectic integration methods
A useful method for understanding discretization error in the numerical solution of ODEs is to compare the system of ODEs with the modified equations obtained through backward error analysis, and using symplectic integration for Hamiltonian ODEs provides more incite into the modified equations. In this paper, the ideas of symplectic integration are extended to Hamiltonian PDEs, and this paves t...
متن کاملBackward error analysis of multiscale symplectic integrators and propagators
Symplectic integrators are used in molecular dynamics simulations for their to excellent long term behavior, due to the existence of the associated shadow Hamiltonian. Improvements in the efficiency of simulations can be obtained by the introduction of multiple timestep methods such as Verlet-I/r-RESPA, but these schemes generally require switches to separate the forces efficiently. The authors...
متن کاملLagrangian Integration with Symplectic Methods
In this short note we show how to obtain Lagrangian integrators from known sym-plectic partitioned Runge-Kutta methods.
متن کاملBackward Error Analysis for Numerical Integrators Backward Error Analysis for Numerical Integrators
We consider backward error analysis of numerical approximations to ordinary diie-rential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modiied diierential equation. A simple recursive deenition of the modiied equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to a...
متن کاملA Modified Multi Time Step Integration for Dynamic Analysis
In this paper new implicit higher order accuracy (N-IHOA) time integration based on assumption of constant time step is presented for dynamic analysis. This method belongs to the category of the multi time step integrations. Here, current displacement and velocity are assumed to be functions of the velocities and accelerations of several previous time steps, respectively. This definition causes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2003
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-003-0458-9