86 citations · 163 across the 22 of their papers we have counts for
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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…
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…
Generalized gaussian bounds for discrete convolution powers
Jean-François Coulombel, Grégory Faye
We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier t…
The Leray-Gårding method for finite difference schemes. II. Smooth crossing modes
Jean-François Coulombel
In [Cou15] a multiplier technique, going back to Leray and Gårding for scalar hyperbolic partial differential equations, has been extended to the context of finite difference schem…
On some stable boundary closures of finite difference schemes for the transport equation
Jean-François Coulombel, Tomas Lundquist
We explore in this article the possibilities and limitations of the so-called energy method for analyzing the stability of finite difference approximations to the transport equatio…