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...

A comprehensive study is presented regarding the stability of the forward explicit integration technique with generalized finite difference spatial discretizations, free of numerical diffusion, applied to the advection-diffusion equation. The modified equivalent partial differential equation approach is used to demonstrate that the approximation is free of numerical diffusion. Two-dimensional r...

A simple method for animation of water waves is presented. The two-dimensional wave equation with damping is used to obtain a finite difference scheme for height distribution. A computational procedure employs explicit time integration. High frame rates are typically obtained for real-time animation of water waves.

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 ...