the transport of dissolved contaminants in groundwater is usually described by the advectiondispersion equation with reaction. several numerical methods for solving the one-dimensional are availableincluding finite difference methods, finite volume methods, and finite element methods. stringent conditions,such as small peclet (pe) and courant (cr) numbers, must be satisfied to ensure the accura...

flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. floods are taken unsteady flows that vary by time and location. equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the saint-venant hypothesis is considered. dynamic wave model as ...

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...

Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategie...

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on ...

In this paper, we consider an implicit finite difference method for solving fuzzy partial differential equations (FPDEs). We present stability of this method and solve the parabolic equation with this scheme.