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Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method

Author

Listed:
  • Emad A. Az-Zo’bi

    (Department of Mathematics and Statistics, Mutah University, Mutah, P.O. Box 7, Al-Karak 61710, Jordan)

  • Kamel Al-Khaled

    (Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan)

  • Amer Darweesh

    (Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan)

Abstract

This work deals with a new modified version of the Adomian-Rach decomposition method (MDM). The MDM is based on combining a series solution and decomposition method for solving nonlinear differential equations with Adomian polynomials for nonlinearities. With application to a class of nonlinear oscillators known as the Lienard-type equations, convergence and error analysis are discussed. Several physical problems modeled by Lienard-type equations are considered to illustrate the effectiveness, performance and reliability of the method. In comparison to the 4th Runge-Kutta method (RK4), highly accurate solutions on a large domain are obtained.

Suggested Citation

  • Emad A. Az-Zo’bi & Kamel Al-Khaled & Amer Darweesh, 2019. "Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method," Mathematics, MDPI, vol. 7(6), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:550-:d:240468
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    References listed on IDEAS

    as
    1. Az-Zo’bi, Emad A. & Yıldırım, Ahmet & AlZoubi, Wael A., 2019. "The residual power series method for the one-dimensional unsteady flow of a van der Waals gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 188-196.
    2. Az-Zo'bi, Emad A. & Dawoud, Kamal Al & Marashdeh, Mohammad, 2015. "Numeric-analytic solutions of mixed-type systems of balance laws," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 133-143.
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    Cited by:

    1. Huda J. Saeed & Ali Hasan Ali & Rayene Menzer & Ana Danca Poțclean & Himani Arora, 2023. "New Family of Multi-Step Iterative Methods Based on Homotopy Perturbation Technique for Solving Nonlinear Equations," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    2. Limei Dai & Xuewen Guo, 2022. "Parabolic Hessian Equations Outside a Cylinder," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    3. Muhammad Aamir Ali & Zhiyue Zhang & Michal Fečkan, 2022. "On Some Error Bounds for Milne’s Formula in Fractional Calculus," Mathematics, MDPI, vol. 11(1), pages 1-11, December.
    4. Jorge E. Macías-Díaz, 2019. "Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme," Mathematics, MDPI, vol. 7(11), pages 1-27, November.

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