In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis ...

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of i...

The Natural Element Method (NEM) is a meshless Galerkin method which has shown promise in the area of computational mechanics. In earlier applications of NEM [1–3], natural neighbor (Sibson) coordinates [4] were used to construct the trial and test functions. Recently, Belikov and co-workers [5] proposed a new interpolation scheme (non-Sibsonian interpolation) based on natural neighbors. In thi...

Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phas...

Numerical solutions of the Helmholtz equation suffer from numerical pollution especially for the case of high wavenumbers. The major component of the numerical pollution is, as has been reported in the literature, the dispersion error which is defined as the phase difference between the numerical and the exact wave. The dispersion error for the meshless methods can be a priori determined at an ...

In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in eithe...

The concept of adaptive shape parameters (ASP) has been presented for solution of incompressible Navier Strokes equations using mesh-free local Radial Basis Functions (RBF). The aim is to avoid ill-conditioning of coefficient matrices of RBF weights and inaccuracies in RBF interpolation resulting from non-optimized shape of basis functions for the cases where data points (or nodes) are not dist...