A heuristic approach to the prediction of a periodic solution for a damping nonlinear oscillator with the non-perturbative technique

The present work attracts attention to obtaining a new result of the periodic solution damped nonlinear Duffing oscillator and Klein–Gordon equation. It is known that frequency response equation in can be derived from homotopy analysis method only absence damping force. We suggest suitable scheme successfully produce without losing coefficient. novel strategy centered on establishing an alternate apart any difficulty handling influence linear term. This alternative was obtained with rank upgrading technique. problem presented using non-perturbative validated by modified perturbation technique successful results toward solution, equation, corresponding stability conditions. methodology yields more effective outcome oscillators. With help this procedure, one analyze many problems domain physical engineering involve oscillators influence. Moreover, all interested plasma authors for modeling different acoustic oscillations plasma.