High Order Hamiltonian Approach to Nonlinear Oscillators

Durmaz S., Altay Demirbağ S., Kaya M. O.

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, vol.11, no.8, pp.565-570, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 8
  • Publication Date: 2010
  • Doi Number: 10.1515/ijnsns.2010.11.8.565
  • Journal Name: INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.565-570
  • Keywords: Nonlinear oscillator, Hamiltonian, high order Hamiltonian approach, Duffing equation, nonlinear oscillator with discontinuity, VARIATIONAL ITERATION METHOD, DISCONTINUITY, BALANCE
  • Istanbul Technical University Affiliated: Yes

Abstract

This paper suggests a high order Hamiltonian approach to nonlinear oscillators. Two examples are given to illustrate the effectiveness of the method. The maximum relative error of Duffing oscillator obtained by He's Hamiltonian approach is 2.22%; while the present approach leads to 0.19% and 0.009% accuracy, respectively, for the second and third approximations.