Fredholm integral equations

Solves a variety of one variable Fredholm integral equations

We present here a program Fie that solves numerically Fredholm integral equations of the second kind on an interval [a,b] to a specified, modest accuracy. Test programs are also included for the various cases. The program TestAll, with no input parameters, can be used to illustrate the various types of integral equations handled by Fie. The kernel 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 finite, 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,\infty).
This program is a joint project between Kendall Atkinson and Larry Shampine. It is described in detail in the jointly written article
"Solving Fredholm integral equations of the second kind in Matlab", ACM Trans. Math. Software, 34 (2008), Issue 4.