We study a projection and upwind finite difference scheme for a combustion model problem. Convergence to weak solutions is proved under the Courant-Friedrichs-Lewy condition. More assumptions are given on the ignition temperature; then convergence to strong detonation wave solutions or to weak detonation wave solutions is proved.

2.1 Examples of conservative schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 The Godunov Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2 The Lax-Friedrichs Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 The local Lax-Friedrichs Scheme . . . . . . . ....

Fast sweeping methods are efficient Gauss–Seidel iterative numerical schemes originally designed for solving static Hamilton–Jacobi equations. Recently, these methods have been applied to solve hyperbolic conservation laws with source terms. In this paper, we propose Lax–Friedrichs fast sweeping multigrid methods which allow even more efficient calculations of viscosity solutions of stationary ...

An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of piecewise deterministic Markov processes [9], including a broader category of random systems. The corresponding Liouville-Master Equation is established and the upwind method is applied to numerical calculation of the distribution function. The convergence of the numerical solutio...

A system composed of two-level systems interacting with a single excitation one-dimensional boson field continuous spectrum, described by Friedrichs (or Friedrichs-Lee) model, can exhibit bound states and resonances; the latter be characterized computing so-called self-energy model. We evaluate an analytic expression, valid for large class dispersion relations coupling functions, such models. A...

The equivalence between the inequalities of Babuška–Aziz and Friedrichs for sufficiently smooth bounded domains in the plane has been shown by Horgan and Payne 30 years ago. We prove that this equivalence, and the equality between the associated constants, is true without any regularity condition on the domain. For the Horgan–Payne inequality, which is an upper bound of the Friedrichs constant ...