On the numerical solution of some semilinear elliptic problems II

In the earlier paper, a Galerkin method was proposed and analyzed for the numerical solution of a Dirichlet problem for a semi-linear elliptic boundary value problem. 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.