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Approximating solutions to the Dirichlet problem in R n using one analytic function
Author(s) -
Whitley R.J.,
Hromadka T.V.,
Horton S.B.
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20515
Subject(s) - mathematics , partial derivative , dirichlet problem , function (biology) , polynomial , analytic function , dirichlet distribution , mathematical analysis , dimension (graph theory) , boundary value problem , dirichlet boundary condition , partial differential equation , variable (mathematics) , pure mathematics , evolutionary biology , biology
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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