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JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS
 

Summary: JOURNAL OF INTEGRAL EQUATIONS
AND APPLICATIONS
Volume 17, Number 3, Fall 2005
SOLVING THE NONLINEAR POISSON EQUATION
ON THE UNIT DISK
KENDALL ATKINSON AND OLAF HANSEN
ABSTRACT. We propose and analyze a numerical method
for solving the nonlinear Poisson equation -u = f(, u) on
the unit disk with zero Dirichlet boundary conditions. The
problem is reformulated as a nonlinear integral equation. We
use a Galerkin method with polynomials as approximations.
The speed of convergence is shown to be very rapid; and ex-
perimentally the maximum error is exponentially decreasing
when it is regarded as a function of the degree of the approx-
imating polynomial.
1. Introduction. In the earlier papers [2, 4] a Galerkin method
was proposed, analyzed, and illustrated for the numerical solution of a
Dirichlet problem for a semi-linear elliptic boundary value problem of
the form
(1)

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences