A MORE ENHANCED DTM FOR THE DUFFING–HARMONIC OSCILLATOR
Mostafa Amir Faishal, Nazmul Sharif, M. Kamrul Hasan
Department of Mathematics, Rajshahi University of Engineering & Technology (RUET),
Kazla, Rajshahi-6204, Bangladesh
Abstract: This paper presented a more efficient differential transform method (DTM) for solving the Duffing–harmonic oscillator. The proposed method significantly minimizes computational effort while maintaining a high level of accuracy in capturing the nonlinear dynamic behavior of the system. The present scheme employs an algebraic series solution that avoids trigonometric functions, thereby reducing computational complexity. Through a detailed comparison study, the performance of the improved DTM was evaluated against a very powerful global residue harmonic balance method (GRHBM) and numerical techniques, demonstrating its effectiveness in generating reliable approximate solutions for Duffing-harmonic oscillators. Thus, the results highlight the method’s capability to handle strong nonlinearities without requiring complex iterative schemes or heavy computational resources. Overall, the findings indicate that the developed DTM serves as a valuable and powerful tool for advancing the analysis of nonlinear dynamic systems and can be readily extended to a wide range of related nonlinear oscillatory models.
Subject Classification: (2010) 34A34, 34B15, 34C15, 34G20
Keywords: Duffing harmonic oscillator; Approximate analytic technique; Differential transform method (DTM); Global residue harmonic balance method (GRHBM).
VOLUME 10 ISSUE 04 2026: 159 – 171