PERIODIC SOLUTIONS FOR CERTAIN NON-SMOOTH OSCILLATORS WITH HIGH NONLINEARITIES


Faydaoglu S., Ozis T.

APPLIED AND COMPUTATIONAL MATHEMATICS, vol.20, no.3, pp.366-380, 2021 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 3
  • Publication Date: 2021
  • Title of Journal : APPLIED AND COMPUTATIONAL MATHEMATICS
  • Page Numbers: pp.366-380
  • Keywords: The Lindstedt-Poincare Method, Parameter Expansions, Modified Homotopy Perturbation Method, Strongly Nonlinear Oscillators, Approximate Solutions, HOMOTOPY PERTURBATION METHOD, EQUATIONS

Abstract

In this paper, we introduce a new adjustment of the Lindstedt-Poincare method combining it homotopy in topology by introducing a linear term with an unknown (variable) frequency and amplitude to be determined further and the solutions are in form of series expansions and maybe converge asymptotically. This adjustment works very well for nonsmooth oscillators with high nonlinearities. Examples given confirm that only one or two iterations lead to high accuracy of the solutions.