Dergiler / Mathematical and Computational Applications / 2010 / Cilt: 15 - Sayı: 5

Variational iteration method for conservative oscillators with complicated nonlinearities

Sayfa
802–809
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Numerical examples shows the feasibility and efficiency of the variational iteration method as well as the presented technique for Fourier series expansion.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The variational iteration method is employed to solve conservative oscillator containing complicated nonlinearities.
📊
Temel Bulgular & Veri:In order to expand the nonlinear terms into truncated Fourier series, an approach of undetermined coefficient is proposed.
💡
Sonuç & Katkı:Numerical examples shows the feasibility and efficiency of the variational iteration method as well as the presented technique for Fourier series expansion.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

The variational iteration method is employed to solve conservative oscillator containing complicated nonlinearities. In order to expand the nonlinear terms into truncated Fourier series, an approach of undetermined coefficient is proposed. Numerical examples shows the feasibility and efficiency of the variational iteration method as well as the presented technique for Fourier series expansion.

🔖

Bu Makaleye Atıf Yap

CHEN, Y. M., MENG, G., LİU, J. K. (2010). Variational iteration method for conservative oscillators with complicated nonlinearities. Mathematical and Computational Applications, Cilt: 15 - Sayı: 5, 802–809. https://ajindex.com/articles/279942

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods Applied Mechanics in Engineering 167, 57-68, 1998
  2. J. H. He, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computer Methods Applied Mechanics in Engineering 167, 69-73, 1998
  3. J. H. He, Variational iteration method—a kind of non-linear analytical technique: some examples, International Journal of Non-linear Mechanics 34, 699-708, 1999
  4. J. H. He, Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation 114, 115-123, 2000
  5. S. Momani, S. Abuasad and Z. Odibat, Variational iteration method for solving nonlinear boundary value problems, Applied Mathematics and Computation 183, 1351-1358, 2006
  6. J. H. He, Variational iteration method-Some recent results and new interpretations, Journal of Computational and Applied Mathematics 207, 3-17, 2007
  7. J. H. He and X. D. Wu, Variational iteration method: New development and applications, Computers Mathematics with Applications 54, 881-894, 2007
  8. J. J. Ramos, On the variational iteration method and other iterative techniques for nonlinear differential equations, Applied Mathematics and Computation 199, 39-69, 2008
  9. M. Rafei, H. Daniali and D. D. Ganji, Variational iteration method for solving the epidemic model and the prey and predator problem, Applied Mathematics and Computation 186, 1701-1709, 2007
  10. V. Marinca, N. Herişanu and C. Bota, Application of the variational iteration method to some nonlinear one-dimensional oscillations, Meccanica 43, 75-79, 2008
  11. V. Marinca and N. Herişanu, Periodic solutions of Duffing equation with strong non-linearity, Chaos, Solitons and Fractals 37, 144-149, 2008
  12. M. Rafei, D. D. Ganji, H. Daniali and H. Pashaei, The variational iteration method for nonlinear oscillators with discontinuities, Journal of Sound and Vibration 305, 614-620, 2007
  13. T. Öziş and A. Yıldırım, A study of nonlinear oscillators with u1/3 force by He’s variational iteration method, Journal of Sound and Vibration 306, 372-376, 2007
  14. P. S. Beran and D. J. Lucia, A reduced order cyclic method for computation of limit cycles, Nonlinear Dynamics 39, 143-158, 2005
  15. D. H. Shou and J. H. He, Application of parameter-expanding method to strongly nonlinear oscillators. International Journal of Nonlinear Sciences and Numerical Simulation, 8(1): 121-124, 2007