On the basis of physical considerations and computational experience, it is poin-ted out that the initial value problem of the Maxwell equations as a set of first order hyperbolic differential equations could become an effective numerical method for the solution of antenna radiation fields. An alternating direction implicit difference scheme is proposed in combination with extrapolated treatment of the conditions on the outer boundary. To demonstrate the potentialities of the proposed method, nu-merical results for a cylindrical antenna are discussed.
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