New approximate solutions to the nonlinear Klein-Gordon equations using perturbation iteration techniques

Bildik N., Deniz S.

Discrete and Continuous Dynamical Systems - Series S, cilt.13, sa.3, ss.503-518, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3934/dcdss.2020028
  • Dergi Adı: Discrete and Continuous Dynamical Systems - Series S
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.503-518
  • Anahtar Kelimeler: Convergence, Nonlinear Klein-Gordon equation, Optimal perturbation iteration method, Quantum mechanics
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this study, we present the new approximate solutions of the nonlinear Klein-Gordon equations via perturbation iteration technique and newly developed optimal perturbation iteration method. Some specific examples are given and obtained solutions are compared with other methods and analytical results to confirm the good accuracy of the proposed methods.We also discuss the convergence of the optimal perturbation iteration method for partial differential equations. The results reveal that perturbation iteration techniques,unlike many other techniques in literature, converge rapidly to exact solutions of the given problems at lower order of approximations.