Symmetric Path Fitted Variational Integrators
نویسندگان
چکیده
منابع مشابه
Phase-fitted discrete Lagrangian integrators
Phase fitting has been extensively used during the last years to improve the behaviour of numerical integrators on oscillatory problems. In this work, the benefits of the phase fitting technique are embedded in discrete Lagrangian integrators. The results show improved accuracy and total energy behaviour in Hamiltonian systems. Numerical tests on the long term integration (10 periods) of the 2-...
متن کاملVariational Integrators
V sequence fxkg. Similar result is also true for quasiNewton methods with trust region (see [16]). Another type of special quasi-Newton methods is that the quasi-Newton matrices are sparse. It is quite often that large-scale problems have separable structure, which leads to special structure of the Hessian matrices. In such cases we can require the quasiNewton matrices to have similar structures.
متن کاملLocal path fitting: A new approach to variational integrators
Abstract. In this work, we present a new approach to the construction of variational integrators. In the general case, the estimation of the action integral in a time interval [qk, qk+1] is used to construct a symplectic map (qk, qk+1) → (qk+1, qk+2). The basic idea here, is that only the partial derivatives of the estimation of the action integral of the Lagrangian are needed in the general th...
متن کاملSpectral variational integrators
In this paper, we present a new variational integrator for problems in Lagrangian mechanics. Using techniques from Galerkin variational integrators, we construct a scheme for numerical integration that converges geometrically, and is symplectic and momentum preserving. Furthermore, we prove that under appropriate assumptions, variational integrators constructed using Galerkin techniques will yi...
متن کاملSpectral-collocation variational integrators
Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can achieve geometric rates of convergence and have a relatively small memory footprint. In this paper, we introduce a general framework to convert a spectral-collocation method into a shootingbased variational integrator for Hamiltonian systems. We also compare the proposed spectral-col...
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: Journal of Physics: Conference Series
سال: 2013
ISSN: 1742-6596
DOI: 10.1088/1742-6596/410/1/012117