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On the Multistage Differential Transformation Method for Analyzing Damping Duffing Oscillator and Its Applications to Plasma Physics

Author

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  • Noufe H. Aljahdaly

    (Department of Mathematics, Faculty of Sciences and Arts-Rabigh Campus, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • S. A. El-Tantawy

    (Center for Physics Research (CPR), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Al-Baha 65431, Saudi Arabia
    Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
    These authors contributed equally to this work.)

Abstract

The multistage differential transformation method (MSDTM) is used to find an approximate solution to the forced damping Duffing equation (FDDE). In this paper, we prove that the MSDTM can predict the solution in the long domain as compared to differential transformation method (DTM) and more accurately than the modified differential transformation method (MDTM). In addition, the maximum residual errors for DTM and its modification methods (MSDTM and MDTM) are estimated. As a real application to the obtained solution, we investigate the oscillations in a complex unmagnetized plasma. To do that, the fluid govern equations of plasma species is reduced to the modified Korteweg–de Vries–Burgers (mKdVB) equation. After that, by using a suitable transformation, the mKdVB equation is transformed into the forced damping Duffing equation.

Suggested Citation

  • Noufe H. Aljahdaly & S. A. El-Tantawy, 2021. "On the Multistage Differential Transformation Method for Analyzing Damping Duffing Oscillator and Its Applications to Plasma Physics," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:432-:d:503590
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    References listed on IDEAS

    as
    1. Alvaro H. Salas & S. A. El-Tantawy & Noufe H. Aljahdaly, 2021. "An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-8, January.
    2. El-Tantawy, S.A., 2016. "Nonlinear dynamics of soliton collisions in electronegative plasmas: The phase shifts of the planar KdV- and mkdV-soliton collisions," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 162-168.
    3. Younghae Do & Bongsoo Jang, 2012. "Enhanced Multistage Differential Transform Method: Application to the Population Models," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, June.
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    Cited by:

    1. Song, Jin & Han, Xiujing, 2024. "Effects of modulation phase on relaxation oscillations in the Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2022. "Novel Approximations to the (Un)forced Pendulum–Cart System: Ansatz and KBM Methods," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    3. Ali, Irfan & Masood, W. & Rizvi, H. & Alrowaily, Albandari W. & Ismaeel, Sherif M.E. & El-Tantawy, S.A., 2023. "Archipelagos, islands, necklaces, and other exotic structures in external force-driven chaotic dusty plasmas," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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