Convergence properties of periodic solutions on a piecewise linear differential equation

In a previous paper, we had proposed an our new method for solving a piecewise linear ordinary differenntial equation. [1] That is, supposing that a resistor and a capacitor are linear but an inductor is piecewise linear, the equation is resulted from a series circuit consisting of the resistor, capacitor and inductor connected with an alternating electromotive force. Since the nonlinearity is piecewise linear the solution can be given by the continuation of each component which is an analytic solution in the corresponding linear interval. But such troublesome continuation prevents us from grasping the whole aspect of the solutions. In this paper, we will show some examples; Approximation of the nonlinear resistance of a superconducting Josephson tunneling device is investigated to obtain one of fundamental data for constructing logic circuits. AC Josephson oscillations are simulated in two different cases where the V-I characteristic is approximated by a piecewise line and nan-approximated method.