Iterative solution of a discrete axially symmetric potential problem

J. Boersma, P. le Grand

Research output: Contribution to journalArticleAcademic

22 Downloads (Pure)

Abstract

The Dirichlet problem for the axially symmetric potential equation in a cylindrical domain is discretized by means of a five-point difference approximation. The resulting difference equation is solved by point or line iterative methods. The rate of convergence of these methods is determined by the spectral radius of the underlying point or line Jacobi matrix. An asymptotic approximation for this spectral radius, valid for small mesh size, is derived.
Original languageEnglish
Pages (from-to)1-12
JournalIndagationes Mathematicae A: Mathematical sciences
Volume78
Issue number1
DOIs
Publication statusPublished - 1975

Fingerprint

Potential Problems
Iterative Solution
Spectral Radius
Difference Approximation
Jacobi Matrix
Line
Asymptotic Approximation
Difference equation
Dirichlet Problem
Rate of Convergence
Mesh
Valid
Iteration

Cite this

@article{9ef80c395aaa4d6e987788f1d39dfe75,
title = "Iterative solution of a discrete axially symmetric potential problem",
abstract = "The Dirichlet problem for the axially symmetric potential equation in a cylindrical domain is discretized by means of a five-point difference approximation. The resulting difference equation is solved by point or line iterative methods. The rate of convergence of these methods is determined by the spectral radius of the underlying point or line Jacobi matrix. An asymptotic approximation for this spectral radius, valid for small mesh size, is derived.",
author = "J. Boersma and {le Grand}, P.",
year = "1975",
doi = "10.1016/1385-7258(75)90008-6",
language = "English",
volume = "78",
pages = "1--12",
journal = "Indagationes mathematicae",
issn = "0019-3577",
publisher = "Elsevier",
number = "1",

}

Iterative solution of a discrete axially symmetric potential problem. / Boersma, J.; le Grand, P.

In: Indagationes Mathematicae A: Mathematical sciences, Vol. 78, No. 1, 1975, p. 1-12.

Research output: Contribution to journalArticleAcademic

TY - JOUR

T1 - Iterative solution of a discrete axially symmetric potential problem

AU - Boersma, J.

AU - le Grand, P.

PY - 1975

Y1 - 1975

N2 - The Dirichlet problem for the axially symmetric potential equation in a cylindrical domain is discretized by means of a five-point difference approximation. The resulting difference equation is solved by point or line iterative methods. The rate of convergence of these methods is determined by the spectral radius of the underlying point or line Jacobi matrix. An asymptotic approximation for this spectral radius, valid for small mesh size, is derived.

AB - The Dirichlet problem for the axially symmetric potential equation in a cylindrical domain is discretized by means of a five-point difference approximation. The resulting difference equation is solved by point or line iterative methods. The rate of convergence of these methods is determined by the spectral radius of the underlying point or line Jacobi matrix. An asymptotic approximation for this spectral radius, valid for small mesh size, is derived.

U2 - 10.1016/1385-7258(75)90008-6

DO - 10.1016/1385-7258(75)90008-6

M3 - Article

VL - 78

SP - 1

EP - 12

JO - Indagationes mathematicae

JF - Indagationes mathematicae

SN - 0019-3577

IS - 1

ER -