We conduct a systematic comparison of spectral methods with some symplectic methods in solving Hamiltonian dynamical systems. Our main emphasis is on the non-linear problems. Numerical evidence has demonstrated that the proposed spectral collocation method preserves both energy and symplectic structure up to the machine error in each time (large) step, and therefore has a better long time behavior
The numerical solution of Hamiltonian PDEs has been the subject of many investigations in the last y...
In this note, numerical methods for a class of Hamiltonian systems which preserve the Hamiltonian ar...
In this note, we consider numerical methods for a class of Hamiltonian systems that preserve the Ham...
Hamiltonian systems typically arise as models of conservative physical systems and have many applica...
We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time sc...
Spectral methods are a popular choice for constructing numerical approximations for smooth problems,...
AbstractWe make qualitative comparisons of fixed step symplectic and variable step nonsymplectic int...
We revisit an algorithm by Skeel et al. [5,16] for computing the modified, or shadow, energy associa...
The purpose of this paper is the derivation of multivalue numerical methods for Hamiltonian problems...
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-ener...
Modulated Fourier expansion is used to show long-time near-conservation of the total and oscillatory...
AbstractWe present the results of a set of numerical experiments designed to investigate the appropr...
In this paper we apply some higher order symplectic numerical methods to analyze the dynamics of 3-s...
At the example of Hamiltonian differential equations, geometric properties of the flow are discussed...
Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and ...
The numerical solution of Hamiltonian PDEs has been the subject of many investigations in the last y...
In this note, numerical methods for a class of Hamiltonian systems which preserve the Hamiltonian ar...
In this note, we consider numerical methods for a class of Hamiltonian systems that preserve the Ham...
Hamiltonian systems typically arise as models of conservative physical systems and have many applica...
We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time sc...
Spectral methods are a popular choice for constructing numerical approximations for smooth problems,...
AbstractWe make qualitative comparisons of fixed step symplectic and variable step nonsymplectic int...
We revisit an algorithm by Skeel et al. [5,16] for computing the modified, or shadow, energy associa...
The purpose of this paper is the derivation of multivalue numerical methods for Hamiltonian problems...
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-ener...
Modulated Fourier expansion is used to show long-time near-conservation of the total and oscillatory...
AbstractWe present the results of a set of numerical experiments designed to investigate the appropr...
In this paper we apply some higher order symplectic numerical methods to analyze the dynamics of 3-s...
At the example of Hamiltonian differential equations, geometric properties of the flow are discussed...
Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and ...
The numerical solution of Hamiltonian PDEs has been the subject of many investigations in the last y...
In this note, numerical methods for a class of Hamiltonian systems which preserve the Hamiltonian ar...
In this note, we consider numerical methods for a class of Hamiltonian systems that preserve the Ham...
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