Piecewise rational approximate solutions of nonlinear transient circuits using adaptive step-size MsDTM-Padé method

In this paper, piecewise rational approximate solutions of nonlinear transient circuits using adaptive step-size multiple step differential transformation method (MsDTM) combined with Padé approximant (MsDTM-Padé) are presented. The principle of the method is introduced and then applied to nonlinear differential equations that describe the behavior of direct current RC transient circuits. Two case studies of transient circuits consisting of an ohmic resistor in series or parallel with a general nonlinear capacitor model characterized by a quintic polynomial voltage-charge dependence are considered. The method can easily achieve convenient rational approximate solutions with any desired degree of accuracy for both the transient and steady state time zones. Numerical results are compared to those obtained by MsDTM, adaptive MsDTM and Fehlberg fourth-fifth-order Runge-Kutta method. The results demonstrate the reliability of the method in solving the considered problems at high accuracy and computational efficiency.