High Order Hamiltonian Approach to Nonlinear Oscillators

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

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, cilt.11, sa.8, ss.565-570, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 8
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1515/ijnsns.2010.11.8.565
  • Dergi Adı: INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.565-570
  • Anahtar Kelimeler: Nonlinear oscillator, Hamiltonian, high order Hamiltonian approach, Duffing equation, nonlinear oscillator with discontinuity, VARIATIONAL ITERATION METHOD, DISCONTINUITY, BALANCE
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

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.