On the numerical solution of some semilinear elliptic problems - II
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 -Delta U = F((.),U). This was converted to a problem on a standard domain and then converted to an equivalent integral equation. Galerkina'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.
elliptic galerkin method integral equation nonlinear