In the present paper, an initial boundary value problem for linear Schrodinger equation including momentum operator ¨ is introduced. This discretized by finite difference method and a scheme presented. Moreover, estimate solution of proposed obtained. Finally, with help estimate, it proved that unconditionally stable convergent.

Phase separation of a two-dimensional van derWaals fluid subject to a gravitational force is studied by numerical simulations based on lattice Boltzmannmethods (LBM) implemented with a finite difference scheme. A growth exponent α=1 is measured in the direction of the external force. PACS: 47.11.-j, 47.20.Hw, 05.70.Ln

This paper considers a fluid dynamic traffic flow model appended with a closure linear velocity-density relationship which provides a first order hyperbolic partial differential equation (PDE) and is treated as an initial boundary value problem (IBVP). We consider the boundary value in such a way that one side of highway treat like there is a traffic controller at that point. We present the ana...

We conduct experimental study on numerical solution of the two dimensional convection-diiusion equation discretized by three nite diierence schemes: the traditional central diier-ence scheme, the standard upwind scheme and the fourth-order compact scheme. We study the computed accuracy achievable by each scheme, the algebraic properties of the coeecient matrices arising from diierent schemes an...

High-order simulation of flows containing shock waves is an extremely difficult task due to the discontinuous changes in flow properties across the shock. The present work investigates a shock-detecting sensor for filtering of high-order compact finitedifference schemes to examine the shock-capturing in direct simulation of NavierStokes solver. Based on the accuracy and minimum dissipation erro...

We introduce a WENO reconstruction based on Hermite interpolation both for semi-Lagrangian and finite difference methods. This WENO reconstruction technique allows to control spurious oscillations. We develop third and fifth order methods and apply them to non-conservative semi-Lagrangian schemes and conservative finite difference methods. Our numerical results will be compared to the usual sem...