In this paper, a semi-implicit finite difference method for the 2-D shallow water equations is derived and applied. A characteristic analysis of the governing equations indicates those terms to be discretised implicitly so that the stability of the method will not depend on the celerity. Such terms are the gradient of the water surface elevation in the momentum equations, and the velocity divergence in the continuity equation. The convective terms are discretised explicitly by using either an upwind or an Eulerian-Lagrangian formula.

Reaction-diffusion systems with cross-diffusion are analyzed here for modeling the population dynamics of epidemic systems. In this paper specific attention is devoted to the numerical analysis and simulation of such systems to show that, far from possible pathologies, the qualitative behaviour of the systems may well interpret the dynamics of real systems.

The convergence quality of the cross-entropy (CE) optimizer relies critically on the mechanism meant for randomly generating data samples, in agreement with the inference drawn in the earlier works--the fast simulated annealing (FSA) and fast evolutionary programming (FEP). Since tracing a near-global-optimum embedded on a nonconvex search space can be viewed as a rare event problem, a CE algorithm constructed using a longtailed distribution is intuitively attractive for effectively exploring the optimization landscape.

In a recent paper we proposed a numerical method to solve a non-standard non-linear second order integro-differential boundary value problem. Here, we answer two questions remained open: we state the order of convergence of this method and provide some sufficient conditions for the uniqueness of the solution both of the discrete and the continuous problem. Finally, we compare the performances of the method for different choices of the iteration procedure to solve the non-standard nonlinearity.