An adaptive numerical method for solving linear Fredholm integral equations of the first kind

A general procedure is presented for numerically solving linear Fredholm integral equations of the first kind. The approximate solution is expressed as a continuous piecewise linear (spline) function. The method involves collocation followed by the solution of an appropriately scaled stabilized linear algebraic system. The procedure may be used iteratively to improve the accuracy of the approximate solution. Several numerical examples are given.Supported in part by the Office of Naval Research under Contract No. NR 044-457.Supported in part by the National Science Foundation under Grant No. GJ-31827.