numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

and Applied Analysis 3 nonlinear term is treated with the Chebyshev collocation method. The time discretization is a classical Crank-Nicholson-leap-frog scheme. Yuan and Wu 43 extended the Legendre dual-Petrov-Galerkin method proposed by Shen 44 , further developed by Yuan et al. 45 to general fifth-order KdV-type equations with various nonlinear terms. The main aim of this paper is to propose ...

We briefly overview the Petrov classification in four dimensions and its generalization to higher dimensions.

a truly meshless local petrov-galerkin (mlpg) method is developed for solving 3d elasto-static problems. using the general mlpg concept, this method is derived through the local weak forms of the equilibrium equations, by using test functions, namely, the heaviside function. the moving least squares (mls) are chosen to construct the shape functions, for the mlpg method. the penalty approximatio...

Recent engineering applications successfully introduced unsymmetric meshless local Petrov-Galerkin (MLPG) schemes. As a step towards their mathematical analysis, this paper investigates nonstationary unsymmetric Petrov-Galerkin-type meshless kernel-based methods for the recovery of L2 functions from finitely many weak data. The results cover solvability conditions and error bounds in negative S...

Using a formalism introduced by Feynman, Deser, Grishchuk, Petrov and Popova, the pseudotensors, such as de ned by Einstein, Tolman, Landau/Lifshitz and M ller, are expessed as gauge dependent tensors in a background space, as the gravitational energy-momentum tensor of Deser, Grishchuk, Petrov and Popova. Using a result obtained by Virbhadra for the energy density in the Reissner-Nordstr om s...

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...