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Kendall E. Atkinson and Larry Shampine: Solving Fredholm integral equations of the second kind in MATLAB, ACM Transactions on Mathematical Software, 34 (2008), article #21 (20 pages), DOI: 10.1145/1377596.1377601. Also in Reports on Computational Mathematics #170 (2006), Dept of Mathematics, University of Iowa. The accompanying program package for Fie is available at http://www.math.uiowa.edu/~atkinson/ftp/Fie.package.
Kendall E. Atkinson and Olaf Hansen: Solving the nonlinear Poisson equation on the unit disk, Journal of Integral Equations & Applications, 17 (2006), pp. 223-241, DOI: 10.1216/jiea/1181075333.
Kendall E. Atkinson and Alvise Sommariva: On the numerical solution of some semilinear elliptic problems - II. Computing: Archives for Scientific Computing 74 (2005), pp. 159-175.
Kendall E. Atkinson and Weimin Han: On the numerical solution of some semilinear elliptic problems, Electronic Transactions on Numerical Analysis 17 (2004), pp. 206-217.
Kendall E. Atkinson: A survey of numerical methods for solving nonlinear integral equations, Journal of Integral Equations & Applications, 4 (1992), pp. 15-46.
Kendall E. Atkinson and Florian Potra: The discrete Galerkin method for nonlinear integral equations, Journal of Integral Equations & Applications, 1 (1988), pp.17-54.
Kendall Atkinson and Alex Bogomolny: The Discrete Galerkin Method for Integral Equations, Mathematics of Computation, 48 (1987), pp. 595-616 and S11-S15.
Kendall Atkinson and Florian Potra: Projection and iterated projection methods for nonlinear integral equations, SIAM Journal of Numerical Analysis 24 (1987), pp. 1352-1373.