A new finite variable difference method with application to locally exact numerical scheme
type: Item
instance of: scholarly article
title: A new finite variable difference method with application to locally exact numerical scheme
zbMATH Open document ID: 0868.65050
author: Katsuhiro Sakai
published in: Journal of Computational Physics
publication date: 1996-07-02T00:00:00Z
review text: A new finite difference scheme for the one-dimensional advection-diffusion-reaction equation is presented and studied. The essence of this method consists of determining the spatial difference, which minimizes the total variance of the solution under the condition that the scheme is always stable. The derived approximation is applied to locally exact numerical schemes (i.e. such that the solution is locally fitted by exponential functions). The optimal spatial differencing is derived in terms of the local mesh Reynold's numbers. Numerous numerical experiments confirm the theoretical findings for large ranges of the parameters.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 881888
zbMATH Keywords: locally exact scheme
zbMATH Keywords: stability
zbMATH Keywords: finite difference
zbMATH Keywords: advection-diffusion-reaction equation
zbMATH Keywords: Reynold's numbers
zbMATH Keywords: numerical experiments
reviewed by: Raytcho D. Lazarov
MaRDI profile type: Publication
full work available at URL: jcph.1996.0061
OpenAlex ID: W1976411400
DOI: 10.1006/JCPH.1996.0061
description: scientific article; zbMATH DE number 881888