On dispersive difference schemes
type: Item
instance of: scholarly article
title: On dispersive difference schemes
zbMATH Open document ID: 0613.65127
DOI: 10.1016/0167-2789(86)90185-5
author: Peter D. Lax
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: In 1944, J. von Neumann proposed a difference scheme for calculating one- dimensional compressible flows with shocks. He conjectured that the approximations converge in the weak sense to the appropriate discontinuous solution of the differential equations. In this note, the author analyzes a special discrete form of the energy equation in the von Neumann scheme, the limit of the solutions of the KdV equation \(U_ t+UU_ x+\epsilon U_{xxx}=0\) as \(\epsilon\) tends to zero and a semidiscrete approximation of the model equation \(U_ t+(0.5U^ 2)_ x=0\) to get reasons that the assertion of von Neuman is wrong.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 3992886
zbMATH Keywords: compressible flows with shocks
zbMATH Keywords: discontinuous solution
zbMATH Keywords: von Neumann scheme
zbMATH Keywords: KdV equation
zbMATH Keywords: semidiscrete approximation
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90185-5
OpenAlex ID: W2068601811
cites work: On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
cites work: Q4321439
cites work: Systems of conservation laws
cites work: The zero dispersion limit of the korteweg-de vries equation for initial potentials with non-trivial reflection coefficient
cites work: The generation of modulated wavetrains in the solution of the Korteweg—de vries equation
description: scientific article; zbMATH DE number 3992886