Continuous Galerkin Petrov time discretization scheme is tested on some Hamiltonian systems including simple harmonic oscillator, Kepler’s problem with different eccentricities and molecular dynamics problem. In particular, we implement the fourth order Continuous Galerkin Petrov time discretization scheme and analyze numerically, the efficiency and conservation of Hamiltonian. A numerical comp...

In this paper, we use Petrov-Galerkin elements such as continuous and discontinuous Lagrange-type k-0 elements and Hermite-type 3-1 elements to find an approximate solution for linear Fredholm integro-differential equations on $[0,1]$. Also we show the efficiency of this method by some numerical examples  

Dual-Petrov-Galerkin approximations to linear third-order equations and the Korteweg-de Vries equation on semi-infinite intervals are considered. It is shown that by choosing appropriate trial and test basis functions the Dual-Petrov-Galerkin method using Laguerre functions leads to strongly coercive linear systems which are easily invertible and enjoy optimal convergence rates. A novel multi-d...

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized Kerr-Schild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied...

The IDR method of Sonneveld and van Gijzen [SIAM J. Sci. Comput., 31:1035–1062, 2008] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML(s)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petro...

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouville operator in the sense of the norm. Spectral Galerkin and Petrov-Galerkin methods for tempered fractional advection problems and tempered ...

A new family of Petrov-Galerkin nite element methods on triangular grids is constructed for singularly perturbed elliptic problems in two dimensions. It uses divergence-free trial functions that form a natural generalization of one-dimensional exponential trial functions. This family includes an improved version of the divergence-free nite element method used in the PLTMG code. Numerical result...

PTB 23 Model F1 Sent./s. Charniak (2000) 89.5 Stanford PCFG (2003) 85.5 5.3 Petrov (2007) 90.1 8.6 Zhu (2013) 90.3 39.0 Carreras (008) 91.1 CJ Reranking (2005) 91.5 4.3 Stanford RNN (2013) 90.0 2.8 PAD 90.6 34.3 PAD (Pruned) 90.5 58.6 CTB 5 Model F1 Charniak (2000) 80.8 Bikel (2004) 80.6 Petrov (2007) 83.3 Zhu (2013) 83.2 PAD 82.4 Experiments Contributions • A phrase-structure parser (PAD) achi...

The purpose of this paper is two-fold. First, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. Alpert [1] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application t...