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
Nystr¨om 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

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa
Oard, Doug - Institute for Advanced Computer Studies & College of Information Studies, University of Maryland at College Park

Collections: Computer Technologies and Information Sciences