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Summary: On the Numerical Solution of Some Semilinear Elliptic Problems II
K. Atkinson, Iowa City and A. Sommariva, Padua
Received March 16, 2004; revised July 22, 2004
Published online: December 20, 2004
Ó Springer-Verlag 2004
Abstract
In the earlier paper [6], a Galerkin method was proposed and analyzed for the numerical solution
of a Dirichlet problem for a semi-linear elliptic boundary value problem of the form
ÀDU ¼ F ðÁ; UÞ. This was converted to a problem on a standard domain and then converted to an
equivalent integral equation. Galerkin's method was used to solve the integral equation, with the
eigenfunctions of the Laplacian operator on the standard domain D as the basis functions. In
this paper we consider the implementing of this scheme, and we illustrate it for some standard
domains D.
AMS Subject Classifications: 65R20, 65N99, 35J65.
Keywords: Elliptic, nonlinear, integral equation, Galerkin method.
1. Introduction
In the earlier paper [6], a Galerkin method is proposed and analyzed for the
numerical solution of a Dirichlet problem for a semi-linear elliptic boundary
value problem of the form
ÀDU ¼ F ðÁ; UÞ on X;
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