A method for the numerical solution of three-dimensional problems of electrodynamics

The present investigation is concerned with a method for obtaining approximate solutions in the case of three-dimensional problems of electrostatics, magnetostatics, and electrodynamics. One class of problems involves the existence of an electrostatic field in a space which contains a number of ideal conductors with given potentials. In another type of problems, a magnetostatic field is present in a space which is partly filled with a magnetic substance. In the third case, a field involving electromagnetic oscillations is considered in a space which is partly filled with ideal conductors. One application of the third class of problems is related to the theory of the diffraction of electromagnetic waves. The solution of the given problems involves a consideration of singular integral equations. The employed algorithm is based on the reduction of the integral equations to a system of linear algebraic equations.