Enclosing the solution of linear Fredholm integral equations of the second kind
A. Gienger · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1999
Abstract We propose a new method to enclose the solution X of a linear Fredholm integral equation of the second kind. Given a certain tolerance ϵ we compute an approximation ẍ for X so that || X — ẍ ||∞ < ϵ holds. The method uses a very efficient algorithm to determine ẍ and interval arithmetic to compute an upper bound for ||x ẍ||∞ On some numerical examples we demonstrate the efficiency of our method.