In this article we analyze the lattice Boltzmann equation (LBE) by using the asymptotic expansion technique. We first relate the LBE to the finite discrete-velocity model (FDVM) of the Boltzmann… Expand

In this paper we establish a connection between a microscopic follow-the-leader model based on ordinary differential equations and a semidiscretization of a macroscopic continuum modelbased on a conservation law.Expand

A mathematical model describing supply chains on a network is introduced. In particular, conditions on each vertex of the network are specified. Finally, this leads to a system of nonlinear… Expand

Simplified PN (SPN) approximations to the equations of radiative heat transfer are derived for optically thick, diffusive systems, and appropriate boundary conditions are formulated. The SPN… Expand

An asymptotic-induced scheme for nonstationary transport equations with the diffusion scaling is developed. The scheme works uniformly for all ranges of mean-free paths. It is based on the asymptotic… Expand

We consider traffic flow models for road networks where the flow is controlled at the nodes of the network. For the analytical and numerical optimization of the control, the knowledge of the gradient… Expand