Approximate solutions for the nonlinear third-order ordinary differential equations

KARAHAN M. M. F.

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, vol.72, no.6, pp.547-557, 2017 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 6
  • Publication Date: 2017
  • Doi Number: 10.1515/zna-2016-0502
  • Journal Name: Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.547-557
  • Keywords: Approximate Analytical Solutions, Multiple Scales Lindstedt-Poincare (MSLP) Method, Nonlinear Third-Order Ordinary Differential Equations, Perturbation Methods, Strongly Nonlinear Systems
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

A new perturbation method, multiple scales Lindstedt-Poincare (MSLP) is applied to jerk equations with cubic nonlinearities. Three different jerk equations are investigated. Approximate analytical solutions and periods are obtained using MSLP method. Both approximate analytical solutions and periods are contrasted with numerical and exact results. For the case of strong nonlinearities, obtained results are in good agreement with numerical and exact ones.