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

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.