On the uniform in small parameter convergence of a weighted scheme for the one-dimensional time-dependent convection-diffusion equation.
type: Item
instance of: scholarly article
title: On the uniform in small parameter convergence of a weighted scheme for the one-dimensional time-dependent convection-diffusion equation.
zbMATH Open document ID: 1122.76353
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-07-04T00:00:00Z
review text: In this paper a weighted two-layer difference scheme for the one-dimensional time-dependent convection-diffusion equation is examined. In this scheme, the first spatial derivative is approximated by the central divided difference. It is shown that, on the piecewise uniform grid condensing in the boundary layer, the scheme is uniformly convergent for \(\sigma\geq0.5\) with respect to small parameter in the sense of the grid norm with an \(O(N^{-2}\ln^{2}N+(\sigma-0.5)\tau+\tau^{2})\) convergence rate, where \(\sigma\) is the scheme parameter, \(N\) is the number of grid points, and \(\tau\) is the time step.
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 76R99
zbMATH DE Number: 1467908
author: Natalia Kopteva
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1467908