In this paper, we consider several high order schemes in one space dimension. In particular, we compare the second order relaxation (<<1) or "relaxed" (=0) schemes of Jin-Xin 4], with the second order Lax-Friedrichs scheme of Nessyahu-Tadmor 6], and with higher order ENO and WENO schemes. This comparison is rst made on Sod shock tube, and then on a very pathological example of a p-system constr...

We present a solver of 3D two-fluid plasma model for the simulation short-pulse laser interactions with plasma. This resolves equations ideal gas closure. also include Bhatnagar-Gross-Krook collision model. Our is based on PseudoSpectral Time-Domain (PSTD) method to solve Maxwell's curl equations. use Strang splitting integrate Euler source term: while are solved composite scheme mixing Lax-Fri...

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exact...

is obtained where A (u) is the Jacobian matrix of the components of / with respect to the components of u. Equation (1.2) is said to be hyperbolic if the eigenvalues of the matrix pi + 6A are real for all real numbers m, 0. Several authors have proposed finite-difference schemes for the numerical integration of (1.1) (or (1.2)). In [6], Lax and Wendroff introduced an explicit scheme which is st...

In this work we present the mathematical model and simulations of a particular wave energy converter, so-called oscillating water column. device, waves governed by one-dimensional nonlinear shallow equations arrive from offshore, encounter step in bottom then into chamber to change volume air activate turbine. The system is reformulated as two transmission problems: one related motion over step...

The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations vehicles. Starting from the paper [21], where single class vehicles proposed, we extend dynamics multi-class leading coupled system conservation laws in two space dimensions. Besides study Riemann problems also present Lax-...

We deal with the numerical investigation of local limit nonlocal conservation laws. Previous experiments seem to suggest that solutions problems converge entropy admissible solution law in singular limit. However, recent analytical results state (i) general convergence does not hold because one can exhibit counterexamples; (ii) be recovered provided viscosity is added both and equations. Motiva...