Solution of the Cubic Duffing Equation via the Differential Transform Method

Authors

  • Najla A. Amazib Department of Mathematics, Faculty of Science, University of Benghazi, Benghazi, Libya
  • Fadwa A. M. Madi Department of Mathematics, Faculty of Science, University of Benghazi, Benghazi, Libya
  • Fawzi A. Abdelwahid Department of Mathematics, Faculty of Science, University of Benghazi, Benghazi, Libya

Keywords:

Ordinary differential equations, Deferential transform method, Jacobian Elliptic functions

Abstract

In this work, we review the dimensional differential transform and introduce a formula for the cubic

non-linear term .  Then, we use the differential transform method, with this formula, to solve the well-known cubic Duffing’s equation.  Next, with the help of Maple program tools, we show that the series solutions obtained by the differential transform method converge rapidly to the Alvaro and Jairo exact solutions, which given in term of the Jacobian elliptic functions.  This shows that the differential transform method is capable to solve non-linear ordinary differential equations, when the non-linear term is given as a polynomial of degree higher than three.

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Published

2025-06-08

Issue

المجلد الثالث، العدد الأول، 2025

Section

Branch of Applied and Natural Sciences

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Najla A. Amazib, Fadwa A. M. Madi, & Fawzi A. Abdelwahid. (2025). Solution of the Cubic Duffing Equation via the Differential Transform Method . Libyan Journal of Contemporary Academic Studies, 3(1), 233-244. https://ljcas.ly/index.php/ljcas/article/view/94