A new perturbation algorithm with better convergence properties: Multiple scales lindstedt poincare method

Pakdemirli M., KARAHAN M. M. F., Boyaci H.

Mathematical and Computational Applications, cilt.14, sa.1, ss.31-44, 2009 (Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 1
  • Basım Tarihi: 2009
  • Doi Numarası: 10.3390/mca14010031
  • Dergi Adı: Mathematical and Computational Applications
  • Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.31-44
  • Anahtar Kelimeler: Perturbation Methods, Lindstedt Poincare method, Multiple Scales method, Numerical Solutions
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

A new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed for the first time. The algorithm combines the advantages of both methods. Convergence to real solutions with large perturbation parameters can be achieved for both constant amplitude and variable amplitude cases. Three problems are solved: Linear damped vibration equation, classical duffing equation and damped cubic nonlinear equation. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces better results for strong nonlinearities. © Association for Scientific Research.