Atomic functions and direct methods for solving singular integral equations of electromagnetics

Atomic functions (AF) are compactly supported infinitely differentiable solutions of functional differential equations, e.g. linear with constant coefficients and linear transformations of an independent variable. In this paper we propose a new numerical technique for solving boundary value problems of electromagnetics. As is known, these problems can be reduced to solving singular integral equations (SIE). For their numerical realization some approximate methods are applicable. We propose a new approach for numerical solving SIE based on AF. Some theoretical questions of existence, uniqueness, and accuracy of an approximate solution are considered. Approximation and computational properties of AF allow us to improve essentially the procedure of SIE evaluation