Approximating solutions to the Dirichlet problem in R n using one analytic function

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 compl...

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Published in:Numerical methods for partial differential equations 2010-11, Vol.26 (6), p.1636-1641
Main Authors: Whitley, R.J., Hromadka, T.V., Horton, S.B.
Format: Article
Language:English
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Summary: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
ISSN:0749-159X
1098-2426
DOI:10.1002/num.20515