An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmannmethod. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have b...

In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting...

We study compact finite difference methods for the Schrödinger-Poisson equation in a bounded domain and establish their optimal error estimates under proper regularity assumptions on wave function ψ and external potential V(x). The CrankNicolson compact finite difference method and the semi-implicit compact finite difference method are both of order O(h4+τ2) in discrete l2 ,H1 and l norms with ...

Finite difference approximation of the nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is studied. The convergence of the finite difference scheme is proved. The rate of convergence of the discrete scheme is given. The decay of the numerical solution is compared with the analytical results proven earlier. Published by Elsevier Inc.

This paper deals with application of the maximum principle for differential equations to the finite difference method for determining upper and lower approximate solutions of the non-linear Burgers’ equation and their error range. In term of mathematical architecture, the paper is based on the maximum principle for parabolic differential equations to establish monotonic residual relations of th...

We study an optimal control problem for viscosity solutions of a Hamilton-Jacobi equation describing the propagation of a one dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the H−1 norm. We prove convergence of a discrete optimal control problem based on a monotone finite differenc...

A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals. We discuss methods f...

The drive mode of fluid body in microchannel is a key in microfluidic control system. ElectroOsmotic MicroPump (EOP) is a microfluidic system which is controlled by electric field with no moving parts. EOPs are attracting increasing attention due to the ease of fluid control in complex microchannels. The theory of forming Electro-Osmotic-Flow (EOF) is analyzed and governing equations are given ...

In this paper, the Specific Absorption Rate (SAR) distribution in a human head irradiated by an obliquely incident electromagnetic plane wave is studied. A simple planar multi-layered structure is used to model the human head. Moreover, the steady state thermal elevation distribution is calculated by solving the bioheat equation using the finite difference time domain (FDTD) method. Both types ...

If we consider a finite difference method simply as a set of equations containing a small parameter (the grid spacing), it is evident that the tools of asymptotic analysis can give us useful information about the method. The applicability of this approach for studying consistency, long time behavior and stability is demonstrated. As example, we use a simple lattice Boltzmann scheme for the 1D a...