A note on the method of analytical regularization. - Fikioris, George
Many problems of electromagnetics are governed by singular integral equations of the first kind. As discussed by Nosich (1999), it is often possible to obtain a different equation describing the problem by applying the method of analytical regularization, and analytically inverting part of the original equation. The transformed equation is of the second kind. Therefore, as a rule, it is usually preferable to apply a numerical method to the transformed equation than to the original one. What appears to be an exception to that rule is discussed in the present paper: under proper conditions, and for a particular numerical method, results obtained by application to the transformed equation are shown to be identical to those obtained by application to the original equation. Some consequences of this equivalence are discussed.
Keywords: Fredholm integral equations; Galerkin method; Regularization; Numerical analysis; Computational electromagnetics; Integral equations