 
Summary: JOURNAL OF INTEGRAL EQUATIONS
AND APPLICATIONS
Volume 4, Number 1, Winter 1992
A SURVEY OF NUMERICAL METHODS FOR SOLVING
NONLINEAR INTEGRAL EQUATIONS
KENDALL E. ATKINSON
ABSTRACT. A survey is given of numerical methods for
calculating fixed points of nonlinear integral operators. The
emphasis is on general methods, ones that are applicable to a
wide variety of nonlinear integral equations. These methods
include projection methods (Galerkin and collocation) and
Nystršom methods. Some of the practical problems related
to the implementation of these methods is also discussed.
All of the methods considered require the solution of finite
systems of nonlinear equations. A discussion is given of some
recent work on iteration methods for solving these nonlinear
equations.
1. Introduction. In the following survey, we consider numerical
methods of a general nature, those that can be applied to a wide variety
of nonlinear integral equations. The integral equations are restricted
