Summary: Electronic Transactions on Numerical Analysis.
Volume 17, pp. 206-217, 2004.
Copyright © 2004, Kent State University.
Kent State University
ON THE NUMERICAL SOLUTION OF SOME SEMILINEAR ELLIPTIC
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.
Key words. elliptic, nonlinear, integral equation, Galerkin method.
AMS subject classifications. 65R20, 65N99, 35J65.
1. Introduction. The purpose of the paper is to propose a general framework for the