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Solving Fredholm Integral Equations of the . . .

By K. E. Atkinson and L. F. Shampine


We present here the algorithms and user interface of a Matlab program, Fie, that solves numerically Fredholm integral equations of the second kind on an interval [a; b] to a specified, modest accuracy. 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; 1)

Topics: General Terms, Algorithms Additional Keywords and Phrases, numerical solution, Matlab
Year: 2007
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