Error analysis when solving Laplace's equation numerically by iteration

Numerical solution methods of Laplace's equation /spl Delta/V=0 when boundary values of potential V are specified abound, and many computer programs employing relaxation techniques, finite-element techniques, etc. have been discussed in the literature. The finite-mesh relaxation method of numer...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on education Vol. 37; no. 1; pp. 84 - 86
Main Author de Wolf, D.A.
Format Journal Article
LanguageEnglish
Published IEEE 01.02.1994
Subjects
Computer errors
Convergence
Electrical engineering
Electromagnetic fields
Error analysis
Iterative methods
Laplace equations
Microcomputers
Physics
Relaxation methods
Online AccessGet full text

Cover

More Information
Summary:Numerical solution methods of Laplace's equation /spl Delta/V=0 when boundary values of potential V are specified abound, and many computer programs employing relaxation techniques, finite-element techniques, etc. have been discussed in the literature. The finite-mesh relaxation method of numerical iteration is discussed in many physics and electrical engineering texts, but little attention is given to the error analysis, which, moreover, is incorrect more often than not in these texts. The authors show that the error in the iterated solution can be found by a relatively simple analysis, and discuss its implications. The authors illustrate the problem by using a very simple PC program that solves the two-dimensional Laplace's equation with Dirichlet conditions on a rectangular boundary.< >
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9359
1557-9638
DOI:10.1109/13.275185