A new technique for obtaining approximate solution of higher order nonlinear differential equation

Abstract

In this study, a new technique is presented combining perturbation method and harmonic balance (HB) method and adopted to investigate a fourth order nonlinear Duffing equation with strong nonlinearity. The advantage of the proposed method is that the method can provide good results even the nonlinearity is strong. The result obtained by the proposed method is compared with the corresponding numerical results to verify the accuracy of the method. The results are also compared with the previous perturbation method results found in literature. Besides, the damped and undamped cases are studied, and the internal resonance is found for undamped case.

Subject Classification:

• 34E05

Keywords:

• Perturbation method
• Harmonic balance method
• Duffing equation