Invariant imbedding and the solution of Fredholm integral equations with displacement Kernels— comparative numerical experiments

摘要

This paper compares the relative efficiencies of the invariant imbedding method with the traditional solution techniques of successive approximations (Picard method), linear algebraic equations, and Sokolov's method of averaging functional corrections in solving numerically two representatives of a class of Fredholm integral equations. The criterion of efficiency is the amount of computing time necessary to obtain the solution to a specified degree of accuracy. The results of this computational investigation indicate that invariant imbedding has definite numerical advantages; more information was obtained in the same length of time as with the other methods, or even in less time. The conclusion emphasized is that a routine application of invariant imbedding may be expected to be computationally competitive with, if not superior to, a routine application of other methods for the solution of some classes of Fredholm integral equations.