IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921007165.html
   My bibliography  Save this article

A new technique for solving a class of strongly nonlinear oscillatory equations

Author

Listed:
  • Alam, M. Shamsul
  • Huq, M. Ashraful
  • Hasan, M. Kamrul
  • Rahman, M. Saifur

Abstract

A new technique has been presented for solving strong nonlinear oscillatory problems. The solution is independent of trigonometric functions, and the determination of unknown coefficients related to the proposed solution is very simple. The method is illustrated by examples. For a large amplitude of oscillation of some nonlinear oscillators, the solution nicely agrees with the corresponding numerical solution.

Suggested Citation

  • Alam, M. Shamsul & Huq, M. Ashraful & Hasan, M. Kamrul & Rahman, M. Saifur, 2021. "A new technique for solving a class of strongly nonlinear oscillatory equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007165
    DOI: 10.1016/j.chaos.2021.111362
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921007165
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111362?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Brahim Benhammouda & Hector Vazquez-Leal & Luis Hernandez-Martinez, 2014. "Modified Differential Transform Method for Solving the Model of Pollution for a System of Lakes," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-12, September.
    2. Beléndez, A. & Beléndez, T. & Márquez, A. & Neipp, C., 2008. "Application of He’s homotopy perturbation method to conservative truly nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 770-780.
    3. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Moghaddam, B.P. & Machado, J.A.T. & Behforooz, H., 2017. "An integro quadratic spline approach for a class of variable-order fractional initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 354-360.
    2. El-Dessoky Ahmed, M.M. & Altaf Khan, Muhammad, 2020. "Modeling and analysis of the polluted lakes system with various fractional approaches," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    4. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Damarla, Seshu Kumar & Kundu, Madhusree, 2015. "Numerical solution of multi-order fractional differential equations using generalized triangular function operational matrices," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 189-203.
    6. Salah Abuasad & Ahmet Yildirim & Ishak Hashim & Samsul Ariffin Abdul Karim & J.F. Gómez-Aguilar, 2019. "Fractional Multi-Step Differential Transformed Method for Approximating a Fractional Stochastic SIS Epidemic Model with Imperfect Vaccination," IJERPH, MDPI, vol. 16(6), pages 1-15, March.
    7. Skwara, Urszula & Mozyrska, Dorota & Aguiar, Maira & Stollenwerk, Nico, 2024. "Dynamics of vector-borne diseases through the lens of systems incorporating fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    8. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    9. BİLDİK, Necdet & DENİZ, Sinan, 2019. "A new fractional analysis on the polluted lakes system," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 17-24.
    10. Yang, Xiao-Jun & Tenreiro Machado, J.A. & Srivastava, H.M., 2016. "A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 143-151.
    11. Kumar, Manoj & Daftardar-Gejji, Varsha, 2019. "A new family of predictor-corrector methods for solving fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    12. Kavyanpoor, Mobin & Shokrollahi, Saeed, 2017. "Challenge on solutions of fractional Van Der Pol oscillator by using the differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 44-45.
    13. Essam R. El-Zahar & Ghaliah F. Al-Boqami & Haifa S. Al-Juaydi, 2024. "Approximate Analytical Solutions for Strongly Coupled Systems of Singularly Perturbed Convection–Diffusion Problems," Mathematics, MDPI, vol. 12(2), pages 1-24, January.
    14. Allahviranloo, T. & Gouyandeh, Z. & Armand, A., 2015. "Numerical solutions for fractional differential equations by Tau-Collocation method," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 979-990.
    15. Yu, Jianping & Jing, Jian & Sun, Yongli & Wu, Suping, 2016. "(n+1)-Dimensional reduced differential transform method for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 697-705.
    16. Kaya, M.O. & Altay Demirbağ, S., 2009. "Application of parameter expansion method to the generalized nonlinear discontinuity equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1967-1973.
    17. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    18. Raja, Muhammad Asif Zahoor & Samar, Raza & Manzar, Muhammad Anwar & Shah, Syed Muslim, 2017. "Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 139-158.
    19. İbrahim Avcı & Nazim I. Mahmudov, 2020. "Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    20. Rehman, Mujeeb ur & Idrees, Amna & Saeed, Umer, 2017. "A quadrature method for numerical solutions of fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 38-49.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007165. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.