Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation
type: Item
instance of: scholarly article
title: Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation
zbMATH Open document ID: 1003.65103
DOI: 10.1016/S0168-9274(01)00146-5
published in: Applied Numerical Mathematics
publication date: 2002-08-22T00:00:00Z
review text: This paper is concerned with the stability constant \(C_{\infty}\) in the maximum norm of the Crank-Nicolson scheme applied to the one dimensional heat equation. By using a sharp resolvent estimate for the discrete Laplacian together with the Cauchy formula, it is shown that \(3\leq C_{\infty}<4.325.\) This bound also holds when the heat equation is considered on a bounded interval along with Dirichlet or Neumann boundary conditions.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 1787727
zbMATH Keywords: stability constant
zbMATH Keywords: heat equation
zbMATH Keywords: Crank-Nicolson scheme
zbMATH Keywords: maximum norm
author: I. Farago
author: César Palencia
describes a project that uses: INTLAB
MaRDI profile type: Publication
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full work available at URL: s0168-9274(01)00146-5
OpenAlex ID: W2082711088
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description: scientific article; zbMATH DE number 1787727