An alternative to the classical methods of analysis of linear antenna systems is proposed. The practice of solving an integral equation directly for an unknown current distribution is replaced by that of solving an integral equation for an unknown intermediate function. This intermediate function is shown to be the forcing function of a differential equation whose closed-form solution yields the unknown current distributions. Numerical results based on the method and contained in this paper compare favorably with those of other investigators both theoretically and by measurement. The method exhibits a convergence rate far superior to that of the classical Pocklington formulation when simple approximating functions and point matching are used, yet the flexibility of the Pocklington formulation is retained. The method is well behaved numerically and convenient for computation.