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.
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Atkinson, K., Sommariva, A. On the Numerical Solution of Some Semilinear Elliptic Problems – II. Computing 74, 159–175 (2005). https://doi.org/10.1007/s00607-004-0094-y
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DOI: https://doi.org/10.1007/s00607-004-0094-y