Effective approximate methods for strongly nonlinear differential equations with oscillations

Marwan Alquran*, Kamel Al-Khaled

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Purpose: This paper proposes the use of different analytical methods in obtaining approximate solutions for nonlinear differential equations with oscillations. Methods: Three methods are considered in this paper: Lindstedt-Poincare method, the Krylov-Bogoliubov first approximate method, and the differential transform method. Results: Figures that are given in this paper give a strong evidence that the proposed methods are effective in handling nonlinear differential equations with oscillations. Conclusions: This study reveals that the differential transform method provides a remarkable precision compared with other perturbation methods.

Original languageEnglish
Article number32
JournalMathematical Sciences
Volume6
Issue number1
DOIs
Publication statusPublished - Dec 2012
Externally publishedYes

Keywords

  • Differential transform method
  • Krylov-Bogoliubov method
  • Lindstedt-Poincare method
  • Nonlinear oscillations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Numerical Analysis
  • Statistics and Probability
  • Information Systems
  • Signal Processing
  • Computer Science Applications

Cite this