Volume 17, pp. 206-217, 2004.

On the numerical solution of some semilinear elliptic problems

Kendall Atkinson and Weimin Han

Abstract

We discuss a general framework for the numerical solution of a family of semilinear elliptic problems whose leading differential operator is the Laplacian. A problem is first transformed to one on a standard domain via a conformal mapping. The boundary value problem on the standard domain is then reduced to an equivalent integral operator equation. We employ the Galerkin method to solve the integral operator equation, using the eigenfunctions of the Laplacian on the standard domain. An error analysis of the method is given.

Full Text (PDF) [152 KB]

Key words

elliptic, nonlinear, integral equation, Galerkin method.

AMS subject classifications

65R20, 65N99, 35J65.

ETNA articles which cite this article

Vol. 37 (2010), pp. 386-412 Kendall Atkinson and Olaf Hansen: A spectral method for the eigenvalue problem for elliptic equations
Vol. 39 (2012), pp. 202-230 Kendall Atkinson and Olaf Hansen: Creating domain mappings

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