Numerical Solution of Non-Fredholm (Singular) Integral Equations by Matrix Inversion

Abstract

It is shown that the simple matrix‐inversion techniques often used in numerically solving linear integral equations with a Fredholm‐Schmidt (i.e., square‐integrable) kernel can also be employed for a wide class of non‐Fredholm (``singular'') equations. This class includes equations the kernel of which is the sum of a Fredholm‐Schmidt kernel and a kernel whose norm (in the operator sense) is less than one. In particular, the integral equations of the so‐called ``new strip approximation'' in particle dynamics belong to this class.