In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common path along the network. We show that the algorithm selects automatically an admissible solution at junctions, hence ad hoc external procedures (e.g., linear pro...

In this paper we fill in the details in the proof of convergence stated in Section 7 of [14], for the locally inertial Godunov method with dynamic time dilation, a numerical method for computing shock wave solutions of the Einstein equations in Standard Schwarzschild Coordinates (SSC). We refer the reader to [14] for an introduction and for the notation assumed at the start here. The main concl...

Here A(u) is a map from a domain U ⊂ Rn into Rn×n, and (x, t) ∈ R×R+. We assume strict hyperbolicity, i. e. the the matrix A(u) has n real and strictly different eigenvalues for each u ∈ U . In the conservative case when A(u) = Df(u) for some map f : U → Rn, Glimm [12] proved global existence of weak entropy solutions of (1) when the data has small total variation and each characteristic field ...

The analysis of diierence methods for initial-boundary value problems was dif-cult during the rst years of the development of computational methods for PDE. The Fourier analysis was available, but of course not suucient for non-periodic boundary conditions. The only other available practical tool was an eigenvalue analysis of the evolution diierence operator Q. Actually, t h e r e w ere deeniti...

We consider a finite difference scheme, called Quickest, introduced by Leonard in 1979, for the convection-diffusion equation. Quickest uses an explicit, Leith-type differencing and third-order upwinding on the convective derivatives yielding a four-point scheme. For that reason the method requires careful treatment on the inflow boundary considering the fact that we need to introduce numerical...

Abstract We discuss the numerical aspects of Boltzmann transport equation (BE) for electrons in semiconductor devices, which is stabilized by Godunov’s scheme. The k-space discretized with a grid based on total energy to suppress spurious diffusion stationary case. Band structures arbitrary shape can be handled. In case, discrete BE yields always nonnegative distribution functions and correspon...