Enclosing the solution of linear Fredholm integral equations of the second kind

We propose a new method to enclose the solution x of a linear Fredholm integral equation of the second kind. Given a certain tolerance epsilon we compute an approximation (x) over bar for x so that parallel to x - (x) over bar parallel to(infinity) less than or equal to epsilon holds. The method uses a very a efficient algorithm to determine (x) over tilde and interval arithmetic to compute an upper bound for parallel to x - (x) over tilde parallel to(infinity). On some numerical examples we demonstrate the efficiency of our method.