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

Necdet Bildik, Sinan Deniz
2018 Discrete and Continuous Dynamical Systems. Series S  
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
more » ... ation iteration techniques,unlike many other techniques in literature, converge rapidly to exact solutions of the given problems at lower order of approximations. 2010 Mathematics Subject Classification. Primary: 70K60, 81Q05, 35Q40; Secondary: 65N1.
doi:10.3934/dcdss.2020028 fatcat:m2axhftv4rb6nk24bl6ggnerba