Treffer: Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation
Title:
Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation
Authors:
Source:
Ninth Seminar on Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-9), 4-9 September 2000, Halle, GermanyApplied numerical mathematics. 42(1-3):133-140
Publisher Information:
Amsterdam: Elsevier, 2002.
Publication Year:
2002
Physical Description:
print, 21 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Equations aux dérivées partielles, problèmes aux valeurs limites, Partial differential equations, boundary value problems, Condition aux limites, Boundary condition, Condiciones límites, Equation chaleur, Heat equation, Ecuación calor, Laplacien, Laplacian, Laplaciano, Modèle 1 dimension, One dimensional model, Modelo 1 dimensión, Méthode Crank Nicolson, Crank Nicolson method, Método Crank Nicolson, Norme, Standards, Norma, Résolvante, Resolvent, Resolvente, Stabilité, Stability, Estabilidad, Somme Riemann, Riemann sum
Document Type:
Konferenz
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Eötvös Loránd University, Kecskemeti u. 10, 1053 Budapest, Hungary
University of Valladolid, Facultad de Ciencias, Prado de la Magdalena s/n, 47005 Valladolid, Spain
University of Valladolid, Facultad de Ciencias, Prado de la Magdalena s/n, 47005 Valladolid, Spain
ISSN:
0168-9274
Rights:
Copyright 2002 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.13824390
Database:
PASCAL Archive
Weitere Informationen
This paper is concerned with the stability constant C∞ in the maximum-norm of the Crank-Nicolson scheme applied to the one-dimensional heat equation. A well known result due to S.J. Serdyukova is that C∞ < 23. In the present paper, by using a sharp resolvent estimate for the discrete Laplacian together with the Cauchy formula, it is shown that 3 ≤ C∞ < 4.325. This bound also holds when the heat equation is considered on a bounded interval along with Dirichlet or Neumann boundary conditions.