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Approximating solutions to the Dirichlet problem in Rn using one analytic function

✍ Scribed by R.J. Whitley; T.V. Hromadka II; S.B. Horton

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 80 KB
Volume: 26
Category: Article
ISSN: 0749-159X
DOI: 10.1002/num.20515

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✦ Synopsis

Abstract

A simpler proof is given of the result of (Whitley and Hromadka II, Numer Methods Partial Differential Eq 21 (2005) 905–917) that, under very mild conditions, any solution to a Dirichlet problem with given continuous boundary data can be approximated by a sum involving a single function of one complex variable; any analytic function not a polynomial can be used. This can be applied to give a method for the numerical solution of potential problems in dimension three or higher. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010

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