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Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators

Author

Listed:
  • Weaam Alhejaili

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Alvaro H. Salas

    (FIZMAKO Research Group, Department of Mathematics and Statistics, Universidad Nacional de Colombia, Manizales 170001, Colombia)

  • Samir A. El-Tantawy

    (Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
    Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Al-Bahah 1988, Saudi Arabia)

Abstract

In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the forced and damped complex Duffing oscillator (I) (FDCDO (I)) and FDCDO (II), are investigated by using some effective analytical and numerical approaches. For the analytical approximation, the two models of the FDCDOs are reduced to two decoupled standard forced and damped Duffing oscillators (FDDOs). After that, both the ansatz method and Krylov–Bogoliubov–Mitropolsky (KBM) approach are applied in order to derive some accurate analytical approximations in terms of trigonometric functions. For the numerical approximations, the finite difference method is employed to analyze the two coupled models without causing them to be decoupled for the original problems. In addition, all obtained analytical and numerical approximations are compared with the fourth-order Runge–Kutta (RK4) numerical approximations. Moreover, the maximum residual distance error (MRDE) is estimated in order to verify the accuracy of all obtained approximations.

Suggested Citation

  • Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2022. "Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4475-:d:985711
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    References listed on IDEAS

    as
    1. Cveticanin, L., 2001. "Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 348-360.
    2. Cveticanin, L., 2003. "Analytic solution of the system of two coupled differential equations with the fifth-order non-linearity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 83-94.
    3. D. V. Hieu & N. Q. Hai & D. T. Hung, 2018. "The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-15, April.
    4. 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.
    5. Mahmoud, Gamal M., 1998. "Approximate solutions of a class of complex nonlinear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 211-222.
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    Cited by:

    1. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2023. "Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators," Mathematics, MDPI, vol. 11(9), pages 1-12, April.

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