86 citations · 163 across the 22 of their papers we have counts for
23 papers
Amplification of numerical wave packets for transport equations with two boundaries
Romain Bonnet-Eymard, Jean-François Coulombel, Grégory Faye
The purpose of this note is to investigate the coupling of Dirichlet and Neumann numerical boundary conditions for the transport equation set on an interval. When one starts with a…
Nonlinear orbital stability of stationary shock profiles for the Lax-Wendroff scheme
Jean-François Coulombel, Grégory Faye
In this article we study the spectral, linear and nonlinear stability of stationary shock profile solutions to the Lax-Wendroff scheme for hyperbolic conservation laws. We first cl…
The local limit theorem for complex valued sequences: the parabolic case
Jean-François Coulombel, Grégory Faye
We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharp…
The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme
Jean-François Coulombel, Antoine Benoit
We study the stability of the two-dimensional Lax-Wendroff scheme with a stabilizer that approximates solutions to the transport equation. The problem is first analyzed in the whol…
The Green's function of the Lax-Wendroff and Beam-Warming schemes
Jean-François Coulombel
We prove a sharp uniform generalized Gaussian bound for the Green's function of the Lax-Wendroff and Beam-Warming schemes. Our bound highlights the spatial region that leads to the…
Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions
Jean-François Coulombel, Grégory Faye
In this article, we consider a class of finite rank perturbations of Toeplitz operators that have simple eigenvalues on the unit circle. Under a suitable assumption on the behavior…