APPROXİMATE SOLUTIONS OF NONLINEAR OSCİLLATORS

Abstract

The modified homotopy perturbation method(MHPM) is used for solving the differential equation of pendulum model. Comparisons are made between the standard HPM and the MHPM. The results show that this method is effective and can obtain high accuracy solutions by only one iteration.

Keywords

• Nonlinear Oscillators,Homotopy Perturbation Method,Modified Homotopy Perturbation Method,Simple pendulum,Approximate solutions

APPROXIMATE SOLUTIONS OF NONLINEAR OSCILLATORS

Öz

The modified homotopy perturbation method (MHPM) is used for solving the differential equation of pendulum model. Comparisons are made between the standard HPM and the MHPM. The results show that this method is effective and can obtain high accuracy solutions by only one iteration. 

Anahtar Kelimeler

• Nonlinear Oscillators,Homotopy Perturbation Method,Modified Homotopy Perturbation Method,Simple Pendulum,Approximate Solutions

References

1. 1. He, J.H., (1999). Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng., 178, 3-4 257–262. http://dx.doi.org/10.1016/S0045-7825(99)00018-3
2. 2. He, J.H., (2003). Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and Computation., 135, 1, 73–79. http://dx.doi.org/10.1016/S0096-3003(01)00312-5
3. 3. Babolian, E., Saeidian, J. and Azizi, A., (2009). Application of Homotopy Perturbation Method to Some Nonlinear Problems. Applied Mathematical Sciences, 3, 45, 2215–2226. http://www.m-hikari.com/ams/ams-password-2009/ams-password45-48-2009/saeidianAMS45-48-2009.pdf