The conversion of Fredholm integral equations to equivalent Cauchy problems— II. computation of resolvents

摘要

A new method is given for computing the resolvent of a large class of Fredholm integral equations. The technique is based on converting the integral equation satisfied by the resolvent to a family of two point boundary value problems. The application of invariant imbedding then gives an equivalent Cauchy problem satisfied by the resolvent kernel. The procedure is compared to previous ones based on the Bellman—Krein equation. It is shown that our method requires fewer equations to integrate if the number of output points on each axis exeeds the bank of the kernel.