Periodic solutions for certain non-smooth oscillators by iterated homotopy perturbation method combined with modified Lindstedt-Poincar, technique


ÖZİŞ T. , AKCI C.

MECCANICA, vol.46, no.2, pp.341-347, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.1007/s11012-010-9312-1
  • Title of Journal : MECCANICA
  • Page Numbers: pp.341-347

Abstract

In this paper, a new technique is introduced by combining Homotopy perturbation method and modified Lindstedt-Poincar, technique to obtain the periodic solutions of certain non-smooth oscillators. In this technique, homotopy perturbation method is re-written in iterative form to linearize perturbation process by homotopy, and then, the modified Lindstedt-Poincar, method is utilized to obtain next approximation for each iteration step. We realize that this new technique works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been confirmed and discussed. Only one or two iterations lead to high accuracy of the solutions. The result obtained and comparison with analytical solution and different methods provide confirmation for the validity of the technique.