Invariant imbedding applied to a class of freholm integral equations

摘要

The objective of this paper is the rigorous derivation of an invariant imbedding algorithm for the solution of the integral equation ø(z)g(z)+γɽ∞0K(∣z-z′∣)ø(z′)dz′øɽø for z⩾0, under suitable restrictions on g, K, and γ. First a set of conditions is determined under which Eq. (1) has a unique solution. The function ø(z) is shown to be approximated almost uniformly for Y=0 and as x→∞ by the solution of