IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4665-d1281616.html
   My bibliography  Save this article

New Numerical and Analytical Solutions for Nonlinear Evolution Equations Using Updated Mathematical Methods

Author

Listed:
  • Abdulghani R. Alharbi

    (Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 42353, Saudi Arabia)

Abstract

This study explores adapted mathematical methods to solve the couple-breaking soliton (BS) equations in two-dimensional spatial domains. Using these methods, we obtained analytical soliton solutions for the equations involving free parameters such as the wave number, phase component, nonlinear coefficient, and dispersion coefficient. The solutions are expressed as hyperbolic, rational, and trigonometric functions. We also examined the impact of wave phenomenon on two-dimensional diagrams and used composite two-dimensional and three-dimensional graphs to represent the solutions. We used the finite difference method to transform the proposed system into a numerical system to obtain numerical simulations for the Black–Scholes equations. Additionally, we discuss the stability and error analysis of numerical schemes. We compare the validity and accuracy of the numerical results with the exact solutions through analytical and graphical comparisons. The methodologies presented in this research can be applied to various forms of nonlinear evolutionary systems because they are appropriate and acceptable.

Suggested Citation

  • Abdulghani R. Alharbi, 2023. "New Numerical and Analytical Solutions for Nonlinear Evolution Equations Using Updated Mathematical Methods," Mathematics, MDPI, vol. 11(22), pages 1-22, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4665-:d:1281616
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4665/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/22/4665/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Manafian, Jalil & Mohammadi-Ivatloo, Behnam & Abapour, Mehdi, 2019. "Lump-type solutions and interaction phenomenon to the (2+1)-dimensional Breaking Soliton equation," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 13-41.
    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. Zhang, Run-Fa & Li, Ming-Chu & Gan, Jian-Yuan & Li, Qing & Lan, Zhong-Zhou, 2022. "Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. Zhang, Run-Fa & Li, Ming-Chu & Albishari, Mohammed & Zheng, Fu-Chang & Lan, Zhong-Zhou, 2021. "Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation," Applied Mathematics and Computation, Elsevier, vol. 403(C).

    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:gam:jmathe:v:11:y:2023:i:22:p:4665-:d:1281616. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.