Error analysis when solving Laplace's equation numerically by iteration

Bibliographic Data

ID20472843
AuthorsDavid Wolf (0000-0002-1566-1237, Virginia Tech, corresponding author), D A de Wolf
Year1994
Volume37
Issue1
Pages84-86
Publication date1994-01-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueIEEE Transactions on Education (JOURNAL)
Journal identifiersISSN: 0018-9359 • E-ISSN: 1557-9638
PublisherIEEE Education Society (PUBLISHER)
DOI10.1109/13.275185
OpenAlexW2155198135
LanguageEN
References cited6

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. >

Boundary value problem · Calculus (dental) · Finite element method · Iterated function · Laplace transform · Laplace's equation · Mathematical analysis · Partial differential equation · Physics · Relaxation (psychology) · Simple (philosophy) · Advanced Numerical Methods in Computational Mathematics · Applied Mathematics · Computer Science · Electromagnetic Simulation and Numerical Methods · Mathematics · Matrix Theory and Algorithms · Numerical Analysis

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