An Accurate Method for Solving the Undamped Duffing Equation with Cubic Nonlinearity

  • Muhammed I. Syam
  • Muhammad Asif Raja
  • Mahmmoud M. Syam
  • H. M. Jaradat
Original Paper


In this paper, we study the strongly nonlinear undamped duffing equation for undamped oscillators. We present the physical and the mathematical model of nonlinear Duffing equation for undamped oscillators. The reproducing kernal Hilbert space method (RKHSM) is employed to compute an approximation to the solution of this problem. The validity of the RKHSM is ascertained by comparing our results with numerical results and other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existences of the solution is proved. In addition, the uniformly convergent of the proposed method is investigated.


Duffing equation Nonlinear boundary value problem Reproducing kernal Hilbert space method 

Mathematics Subject Classification

76A05 76W05 76Z99 65L05 


Compliance with Ethical Standards

Conflicts of interest

The authors declare that there is no conflict of interests regarding the publication of the paper.


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Copyright information

© Springer (India) Private Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Muhammed I. Syam
    • 1
  • Muhammad Asif Raja
    • 2
  • Mahmmoud M. Syam
    • 3
  • H. M. Jaradat
    • 4
  1. 1.Department of Mathematical Sciences College of ScienceUAE UniversityAl-AinUnited Arab Emirates
  2. 2.Department of Electrical EngineeringCOSATS Institute of Information TechnologyAttockPakistan
  3. 3.Department of Mechanical EngineeringUAE UniversityAl-AinUnited Arab Emirates
  4. 4.Department of MathematicsAl al-Bayt UniversityMafraqJordan

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