Result: Stability in the numerical solution of the heat equation with nonlocal boundary conditions

Title:
Stability in the numerical solution of the heat equation with nonlocal boundary conditions
Authors:
BOROVYKH, Natalia
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):17-27
Publisher Information:
Amsterdam: Elsevier, 2002.
Publication Year:
2002
Physical Description:
print, 26 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 différentielles, Ordinary differential equations, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Approximation numérique, Numerical approximation, Condition aux limites, Boundary condition, Condiciones límites, Convergence, Convergencia, Discrétisation, Discretization, Discretización, Equation chaleur, Heat equation, Ecuación calor, Equation intégrale, Integral equation, Ecuación integral, Intégrale, Integral, Méthode Crank Nicolson, Crank Nicolson method, Método Crank Nicolson, Méthode numérique, Numerical method, Método numérico, Méthode à pas, Step method, Método a paso, Norme, Standards, Norma, Résolvante, Resolvent, Resolvente, Solution numérique, Numerical solution, Stabilité numérique, Numerical stability, Estabilidad numérica, Stabilité, Stability, Estabilidad
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Mathematical Institute, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, Netherlands
ISSN:
0168-9274
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=13824383
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
Notes:
Mathematics
Accession Number:
edscal.13824383
Database:
PASCAL Archive

Further Information

This paper deals with numerical methods for the solution of the heat equation with integral boundary conditions. Finite differences are used for the discretization in space. The matrices specifying the resulting semidiscrete problem are proved to satisfy a sectorial resolvent condition, uniformly with respect to the discretization parameter. Using this resolvent condition, unconditional stability is proved for the fully discrete numerical process generated by applying A(θ)-stable one-step methods to the semidiscrete problem. This stability result is established in the maximum norm; it improves some previous results in the literature in that it is not subject to various unnatural restrictions which were imposed on the boundary conditions and on the one-step methods.