A method for calculating generalized solutions to the one-dimensional linear advection equation
type: Item
instance of: scholarly article
zbMATH Open document ID: 0969.65082
publication date: 2001-06-10T00:00:00Z
full work available at URL: eng
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 1603344
zbMATH Keywords: transport equation
zbMATH Keywords: generalized solution
zbMATH Keywords: finite-difference method
zbMATH Keywords: higher-order approximation
zbMATH Keywords: linear advection equation
MaRDI profile type: Publication
author: V. M. Fomin
title: A method for calculating generalized solutions to the one-dimensional linear advection equation
published in: Vychislitel'nye Tekhnologii
review text: The author develops a numerical method for calculating generalized solutions to the transport equation in the case of one-dimensional spatial variable. He constructs a class of numerical schemes which guarantee a higher-order approximation to generalized solutions for the transport equation. The construction of these schemes is based on expansion of the generalized solutions under consideration into the sum of smooth and singular parts. The advantage of the method suggested is that the schemes make it possible to avoid loss of accuracy which is inevitable for almost all methods in practice.
description: scientific article; zbMATH DE number 1603344