[PDF] Top 20 On variational and symplectic time integrators for Hamiltonian systems

... for time integration is given using weighted residuals for general nonlinear ordinary differential ...(implicit) symplectic Runge–Kutta methods, sat- isfying the symplectic condition by ...discrete ... See full document

... [1] Hamiltonian systems described by linear, constant-coefficient ordinary differential equations (in the following ‘‘Hamiltonian 1D systems’’) were studied using the formalism of quadratic- ... See full document

... general symplectic or multi-symplectic integrator for the bi- Hamiltonian systems with nonconstant structure in (1), one can look for energy preserving ...the symplectic and ... See full document

... linear Hamiltonian systems at resonance with periodic nonlinearity is ...such systems is obtained by means of variational methods, saddle point theorem, and an index theory for second-order ... See full document

... Tang, CL, Wu, XP: Periodic solutions for a class of nonautonomous subquadratic second order Hamiltonian systems.. Chang, KC: Variational methods for non-differentiable functionals and the[r] ... See full document

... numerical integrators that approximate evolution of the system may be ...the integrators converge to exact solutions of the equations, for finite time steps the behavior of various integrators ... See full document

... Because the exact solution is known for all the sample problems it is easy to impose whatever boundary condition are desired on any spatial domain. The domains were chosen so the solutions were not periodic or symmetric ... See full document

... Finally, I thank my supervisor Robert McLachlan. I could not have wished for a better supervisor. He took me on with no reservations, even though I had been out of academia for 15 years, and I quit half-way through my ... See full document

... servative systems in mechanics, physics, biology, and chemistry fit the Hamiltonian ...The Hamiltonian flow or solution to a Hamiltonian system pre- serves the Hamiltonian and the ... See full document

... be time consuming compared to the symplectic integrators like the mid-pint rule and implicit Runge-Kutta methods of Gauss-Legendre ...the Hamiltonian is polynomial as the coupled KdV equations ... See full document

... Geometric integrators, which are well designed numerical schemes preserving some in- variant quantities of a differential equation, have been developed by many authors for par- ticular types of differential ... See full document

... a time step t = ...the symplectic scheme is much more accurate regarding the preservation ...the Hamiltonian increases linearly and is about ... See full document

... geometric integrators be formulated and implemented for collision problems? In fact, the algorithms developed in this work show how a symplectic method can be constructed for nonsmooth systems so ... See full document

... the Hamiltonian character migrate in the discrete-time case: this may be achieved if the discretization step is chosen as T/N , where T is the period in the continuous-time case and N is a ... See full document

... energetic variational approaches for hydrodynamic systems of complex ...energetic variational approaches, the least action principle (LAP) with action functional gives the Hamiltonian parts ... See full document

... Hamiltonian systems are an important class of nonlinear systems commonly used to model conser- vative physical systems, ...conservative systems, particularly conservation of the ... See full document

... coordinate-dependent integrators that can be unattractive theoretically as well as impractical: for instance, using Euler angles for rigid body integrators has the difficulty that we may spend most of our ... See full document

... These advantages of nonstandard finite difference methods have been shown in many numerical applications. González-Parra et al. [, ] developed some nonstandard finite difference methods to preserve the positivity ... See full document

... modified Hamiltonian is used to study the nonlinear stability of symplectic integrators, espe- cially for nonlinear ...mechanical systems for exponentially long ... See full document

... discrete variational principle was restated to obtain the discrete balance of linear momentum, energy and configurational forces as Euler–Lagrange ...elemental time step, and by rearranging the positions of ... See full document