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Summary: Solving Fredholm Integral Equations of the
Second Kind in Matlab
K. E. Atkinson
Dept of Mathematics
University of Iowa
L. F. Shampiney
Dept of Mathematics
Southern Methodist University
May 5, 2007
Abstract
We present here the algorithms and user interface of a Matlab pro-
gram, Fie, that solves numerically Fredholm integral equations of the
second kind on an interval [a; b] to a speci...ed, modest accuracy. The ker-
nel function K(s; t) is to be moderately smooth on [a; b] [a; b] except
possibly across the diagonal s = t. If the interval is ...nite, Fie provides
for kernel functions that behave in a variety of ways across the diagonal,
viz. K(s; t) may be smooth, have a discontinuity in a low-order derivative,
have a logarithmic singularity, or have an algebraic singularity. Fie also
solves a large class of integral equations with moderately smooth kernel
function on [0; 1).
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