Semi-analytical solutions of nonlinear transient circuits using differential transform based methods

In this paper, semi-analytical solutions of nonlinear transient circuits using differential transform based methods are presented. The methods are Multiple-Step Differential Transform Method (MsDTM) and MsDTM with Padé approximants (MsDTM-P). The error and stability analysis of the methods are presented. The methods are applied to the nonlinear differential equation which describes a direct current RC circuit, taking into account the effect of a nonlinear capacitor on the charge of the capacitor. Comparing the results obtained by the methods and some other peer methods revealed that the MsDTM-P is more suitable for solving the considered problem because of its stability and higher accuracy.