On the solutions of equations for nonlinear resistive networks

Several theorems are proved concerning the solutions of equations that arise in the study of resistive nonlinear electrical networks. The first, an existence and uniqueness theorem, applies to equations describing an interesting class of networks which includes certain active and nonreciprocal networks for which the existence and uniqueness of solutions has not previously been established. A method of computing bounds on the location of the solutions is given, and two iterative techniques are presented for computing the solutions. It is proved that the iterative techniques converge for a subclass of the equations which also includes equations describing certain active and nonreciprocal networks. Finally, the rate of convergence of the iterative techniques is compared with that of another well-known iterative technique and some practical computational aspects are pointed out. Computations for two example problems, not reported here, were carried out to show the practicality of applying these iterative techniques to the equations of specific networks.