On the Numerical Solution of Fredholm Integral Equations of the First Kind

Two previously given methods for the numerical solution of Fredholm integral equations of the first kind are investigated by the use of polynomial spline functions. As a byproduct a new method is presented for obtaining the eigensolutions of the kernel function. From numerical experiments zero order regularization appears to give more accurate results than higher orders. A comparison is made as to the relative accuracy and speed of the two methods. A scheme is presented to enable a choice to be made, from the set of truncated solutions, as to which member is closest to the solution of the integral equation.