An efficient treatment is developed for the Schrödinger equation with a class of local absorbing boundary conditions, which are obtained by high order Padé expansions. These boundary conditions are significant in the simulation of open quantum devices. Based on the finite difference approximation in the interior domain, we construct a spectral collocation layer on the cell near the artificial b...

We propose a Legendre-Petrov-Galerkin Chebyshev spectral collocation method for initial value problems (IVPs) of second-order nonlinear ordinary differential equations (ODEs). The is applied to time discretization and the term dealt with method. scheme results in simple algebraic system by choosing appropriate basis functions. Optimal error estimates $ L^2 $-norm single multiple interval method...

In this paper, a new algorithm based on using Chebyshev waveletoperational matrix of integration instead operational derivativeto find the approximate solution two points boundary value problem.Wavelet first with aid collocation method employed totransform differential equation its condition to systemof linear algebraic equations. A very high level accuracy explicitlyreflected by proposed examp...

We present a numerical approach for generalised Korteweg-de Vries (KdV) equations on the real line. In spatial dimension we compactify line and apply Chebyshev collocation method. The time integration is performed with an implicit Runge-Kutta method of fourth order. Several examples are discussed: initial data bounded but not vanishing at infinity as well satisfying Faddeev condition, i.e. slow...

1 Abstract In this paper we study thermoconvective instabilities appearing in a fluid which is in a cylindrical annulus heated laterally. As soon as the applied temperature gradient reaches a critical value a stationary bifurcation takes place. The problem is modelized with the original Navier Stokes equations by keeping pressure with appropriate boundary conditions. This is a low order formula...