On the numerical solution of some semilinear elliptic problems - II

Authors:
K. Atkinson;A. Sommariva
Affiliations:
Departments of Mathematics and Computer Science, The University of Iowa, Iowa City, IA;Department of Pure and Applied Mathematics, University of Padua, Padua, Italy
Venue:
Computing
Year:
2005

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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 -ΔU = F-U. 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.