We provide Matlab scripts and functions for solving numerically nonlinear Fredholm integral equations of the second kind on an interval [a,b]. Our method simply consists in evaluating the integral by a quadrature rule, then solving iteratively the corresponding system of nonlinear equations obtained by collocation, and finally in accelerating these iterations by sequence transformations, namely the topological epsilon-transformations, implemented via a simplified recursive algorithm. We also use a restarting procedure for this nonlinear system. Thus, our procedures are quite simple and easy to implement.
The Matlab scripts AM_eqint (Acceleration Method) and RM_eqint (Restarted Method) reproduce the Examples 1 to 6 of the paper "Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations", J. Integral Equations Appl, to appear. They also provide ten other additional examples coming out from the literature (see the references in the function help_eqint) and allow to try them with other values of the various parameters, and make new experiments.
For the sequence transformations needed, the Matlab toolbox EPSfun, which is freely available as na44 from the numeralgo library of netlib, has to be first installed. It is useful, for making new experiments, to read carefully the userguide provided with the toolbox EPSfun.
After that, simply download the files from the Matlab file exchange site, store them in a separate directory, run one of the two scripts, and enjoy!
The software is a joint work of
Claude Brezinski (email@example.com) and
Michela Redivo-Zaglia (firstname.lastname@example.org).
Download apps, toolboxes, and other File Exchange content using Add-On Explorer in MATLAB.