A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom

Abstract

A novel technique is proposed for finding an approximate solution of the strongly nonlinear ordinary differential equation for the charged damped pendulum with one degree of freedom. The method relies on a transformation of the governing nonlinear differential equation that keeps unchanged the order of the highest derivative, in conjunction with a modified homotopy perturbation technique (MHPM). Only quadratic damping is considered for the numerical computations. To validate the used technique, the obtained results are compared to those arising from a numerical solution by Runge–Kutta of the fourth order (RK4) and by finite differences (FD). Good agreement between the two solutions is reached when quadratic damping is suppressed. In the presence of damping, agreement takes place only for a rather limited range of times. Plots of the analytical solutions are provided for both cases. The proposed method may be used to analyze a wide class of nonlinear differential equations.