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 ...

In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β ∈ (1,2]. We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are ana...

In this paper, thermal effects of laser irradiance on biological tissue is investigated using computer simulations. Earlier attempts in this field made use of finite difference and finite element techniques. Here a novel approach is adopted to improve the results. The effect of our implicit approach on the convergence procedure and accuracy of results, with different timing steps, is explor...

The evolution in space and time of crime risk and criminal density is modeled by a coupled system of partial differential equations, and solved with a semi-implicit method using finite differences. Under appropriate conditions, isolated stationary hot spots of high criminal activity form.

This article deals with finitedifference schemes of two-dimensional heat transfer equations with moving boundary. The method is suggested by solving sample problem in two-dimensional solidification of square prism. The finite-difference scheme improved for this goal is based on the Douglas equation. The results are devised for a two-dimensional model and crosschecked with results of the earlier...

We propose an analytical approach to calculate the effective dielectric function of proteins in aqueous solution. The screening effect if quantified by a measure of enclosure which is based on the distribution of solute atomic volumes around a pair of charges in a macromolecule. For protein conformations that vary significantly in size and shape, a comparison with finite difference Poisson calc...

In this paper, two different finite differences schemes are presented for numerical solution of two-dimensional moving boundary problem. The methods are illustrated by solving sample problem in two-dimensional solidification of the square prism. The finite difference schemes developed for this purpose are based on the method of lines using interpolation polynomials. The fully explicit method de...

in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...