29 citations · 47 across the 12 of their papers we have counts for
5 papers · 1 filter
A Numerical Approach to Scalar Nonlocal Conservation Laws
Paulo Amorim, Rinaldo M. Colombo, Andreia Teixeira
We address the study of a class of 1D nonlocal conservation laws from a numerical point of view. First, we present an algorithm to numerically integrate them and prove its converge…
Convergence of a numerical scheme for a coupled Schrödinger--KdV system
Paulo Amorim, Mário Figueira
We prove the convergence in a strong norm of a finite difference semi-discrete scheme approximating a coupled Schrödinger--KdV system on a bounded domain. This system models the in…
Convergence of a finite difference method for the KdV and modified KdV equations with data
Paulo Amorim, Mário Figueira
We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in ), wi…
Convergence of numerical schemes for short wave long wave interaction equations
Paulo Amorim, Mário Figueira
We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schrödinger equation coupled with a hyperbolic conservation law. This sy…
Finite volume schemes on Lorentzian manifolds
Paulo Amorim, Philippe G. LeFloch, Bawer Okutmustur
We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishe…