Superconvergence of Galerkin variational integrators
نویسندگان
چکیده
We study the order of convergence Galerkin variational integrators for ordinary differential equations. approximate a (Lagrangian) problem by restricting space curves to set polynomials degree at most $s$ and approximating action integral using quadrature rule. show that, if rule is sufficiently accurate, thus obtained $2s$.
منابع مشابه
Generalized Galerkin Variational Integrators
We introduce generalized Galerkin variational integrators, which are a natural generalization of discrete variational mechanics, whereby the discrete action, as opposed to the discrete Lagrangian, is the fundamental object. This is achieved by approximating the action integral with appropriate choices of a finite-dimensional function space that approximate sections of the configuration bundle a...
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 کاملSuperconvergence of Galerkin Solutions for Hammerstein Equations
In the present paper, we discuss the superconvergence of the interpolated Galerkin solutions for Hammerstein equations. With the interpolation post-processing for the Galerkin approximation xh, we get a higher order approximation I 2r−1 2h xh, whose convergence order is the same as that of the iterated Galerkin solution. Such an interpolation post-processing method is much simpler than the iter...
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: IFAC-PapersOnLine
سال: 2021
ISSN: ['2405-8963', '2405-8971']
DOI: https://doi.org/10.1016/j.ifacol.2021.11.098