Explicit formula for the limit of a difference approximation
type: Item
instance of: scholarly article
title: Explicit formula for the limit of a difference approximation
zbMATH Open document ID: 0715.65068
DOI: 10.1215/S0012-7094-90-06116-2
author: K. T. Joseph
author: G. D. Veerappa Gowda
published in: Duke Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The conservation law \(u_ t+(\log (a \exp (a)+b \exp (-a)))_ x=0\) with \(a>0\), \(b>0\), \(a+b=1\), \(u(x,0)=u_ 0(x)\) is considered in the quarter plane \(x>0\), \(t>0\). An approximate solution of this problem is constructed using the difference scheme \(u_ k^{n+1}=u^ n_ k+(\Delta t/\Delta x)(g(u^ n_{k-1},u^ n_ k)-g(u^ n_ k,u^ n_{k+1})),\) \(u^ 0_ k=u_ 0(k\Delta x),\quad u^ n_ 0=\lambda (n\Delta t),\) where \(g(u,v)=\log (a \exp (u)+b \exp (v)).\) The main result of the paper consists in obtaining an expression for the solution of the difference equations and its limit when the temporal and spatial steps tend to zero.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 4178681
zbMATH Keywords: limit of a difference approximation
zbMATH Keywords: conservation law
zbMATH Keywords: difference scheme
reviewed by: A. I. Tolstykh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4178681