On the Numerical Solution of Some Semilinear Elliptic Problems

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 U = 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. 1 Introduction In the earlier paper [6] a Galerkin method is proposed and analyzed for the numerical solution of a Dirichlet problem for a semi-linear elliptic boundary Keywords: elliptic, nonlinear, integral equation, Galerkin method yAMS subject classi…cation Primary: 65R20; Secondary: 65N99, 35J65

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Cite this paper

@inproceedings{Sommariva2004OnTN, title={On the Numerical Solution of Some Semilinear Elliptic Problems}, author={Alvise Sommariva}, year={2004} }