 
Summary: THE NUMERICAL SOLUTION OF A
NONLINEAR BOUNDARY INTEGRAL
EQUATION ON SMOOTH SURFACES
Kendall E. Atkinson
Dept of Mathematics
University of Iowa
Iowa City, Iowa 52242
USA
July 24, 1994
Abstract
We study aboundary integral equation method for solving Laplace's
equation u = 0 with nonlinear boundary conditions. This nonlinear
boundary value problem is reformulated as a nonlinear boundary in
tegral equation, with u on the boundary as the solution being sought.
The integral equation is solved numerically by using the collocation
method, with piecewise quadratic functions used as approximations
to u. Convergence results are given for the cases that (1) the origi
nal surface is used, and (2) the surface is approximated by piecewise
quadratic interpolation. In addition, we de ne and analyze a twogrid
iteration method for solving the nonlinear system that arises from the
