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.
On the numerical solution of some semilinear elliptic problems II
SOMMARIVA, ALVISE
2005
Abstract
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.File in questo prodotto:
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