Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method

Abstract

The modified differential transform method (MDTM), Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain.

Keywords

• forced duffing oscillator
• forced van der Pol Oscillator
• Padé approximant
• laplace transform
• semi-analytical solution