IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v197y2022icp277-290.html
   My bibliography  Save this article

Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation

Author

Listed:
  • Bulut, Fatih
  • Oruç, Ömer
  • Esen, Alaattin

Abstract

In this paper, we are going to utilize newly developed Higher Order Haar wavelet method (HOHWM) and classical Haar wavelet method (HWM) to numerically solve the Regularized Long Wave (RLW) equation. Spatial variable of the RLW equation is treated with HOHWM and HWM separately. On the other hand temporal variable is discretized by finite differences combined with Strang splitting approach. The presented methods applied to three different test problems and the obtained results are given in tables as well as depicted in figures. The obtained results are compared with analytical results wherever they exist. The error norms L2 and L∞ and invariants I1, I2 and I3 are used to show the accuracy of the methods when comparing the present results with those in the literature.

Suggested Citation

  • Bulut, Fatih & Oruç, Ömer & Esen, Alaattin, 2022. "Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 277-290.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:277-290
    DOI: 10.1016/j.matcom.2022.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422000593
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.02.006?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. Lepik, Ü., 2005. "Numerical solution of differential equations using Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 127-143.
    2. S. Kutluay & A. Esen, 2006. "A finite difference solution of the regularized long-wave equation," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-14, March.
    3. Ömer Oruç & Alaattin Esen & Fatih Bulut, 2016. "A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(09), pages 1-16, September.
    4. Hsiao, Chun-Hui, 1997. "State analysis of linear time delayed systems via Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(5), pages 457-470.
    5. Mart Ratas & Jüri Majak & Andrus Salupere, 2021. "Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method," Mathematics, MDPI, vol. 9(21), pages 1-12, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Khater, Mostafa M.A., 2023. "Computational simulations of propagation of a tsunami wave across the ocean," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Ahsan, Muhammad & Bohner, Martin & Ullah, Aizaz & Khan, Amir Ali & Ahmad, Sheraz, 2023. "A Haar wavelet multi-resolution collocation method for singularly perturbed differential equations with integral boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 166-180.
    3. Swati, & Singh, Mandeep & Singh, Karanjeet, 2023. "An efficient technique based on higher order Haar wavelet method for Lane–Emden equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 21-39.
    4. Amit Kumar & Ayub Khan & Abdullah Abdullah, 2024. "Fibonacci Wavelet Collocation Method for Solving Dengue Fever SIR Model," Mathematics, MDPI, vol. 12(16), pages 1-14, August.
    5. Jangid, Komal & Singh, Bhagwan & Mukhopadhyay, Santwana, 2024. "Legendre wavelet collocation method for investigating thermo-mechanical responses on biological tissue during laser irradiation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 404-423.

    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. Igor Sinitsyn & Vladimir Sinitsyn & Eduard Korepanov & Tatyana Konashenkova, 2022. "Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions," Mathematics, MDPI, vol. 10(9), pages 1-14, May.
    2. Mart Ratas & Jüri Majak & Andrus Salupere, 2021. "Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method," Mathematics, MDPI, vol. 9(21), pages 1-12, November.
    3. Igor Sinitsyn & Vladimir Sinitsyn & Eduard Korepanov & Tatyana Konashenkova, 2021. "Wavelet Modeling of Control Stochastic Systems at Complex Shock Disturbances," Mathematics, MDPI, vol. 9(20), pages 1-15, October.
    4. Bashan, Ali & Yagmurlu, Nuri Murat & Ucar, Yusuf & Esen, Alaattin, 2017. "An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 45-56.
    5. Pathak, Maheshwar & Joshi, Pratibha & Nisar, Kottakkaran Sooppy, 2022. "Numerical study of generalized 2-D nonlinear Schrödinger equation using Kansa method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 186-198.
    6. Huang, Yifei & Peng, Gang & Zhang, Gengen & Zhang, Hong, 2023. "High-order Runge–Kutta structure-preserving methods for the coupled nonlinear Schrödinger–KdV equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 603-618.
    7. Pervaiz, Nosheen & Aziz, Imran, 2020. "Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Ngondiep, Eric, 2024. "A high-order combined finite element/interpolation approach for multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 560-577.
    9. Ihtisham Ul Haq & Numan Ullah & Nigar Ali & Kottakkaran Sooppy Nisar, 2022. "A New Mathematical Model of COVID-19 with Quarantine and Vaccination," Mathematics, MDPI, vol. 11(1), pages 1-21, December.
    10. Jahangiri, Ali & Mohammadi, Samira & Akbari, Mohammad, 2019. "Modeling the one-dimensional inverse heat transfer problem using a Haar wavelet collocation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 13-26.
    11. Ahsan, Muhammad & Bohner, Martin & Ullah, Aizaz & Khan, Amir Ali & Ahmad, Sheraz, 2023. "A Haar wavelet multi-resolution collocation method for singularly perturbed differential equations with integral boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 166-180.
    12. Hsiao, C.H., 2004. "Haar wavelet approach to linear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 561-567.
    13. Awati, Vishwanath B. & Goravar, Akash & N., Mahesh Kumar, 2024. "Spectral and Haar wavelet collocation method for the solution of heat generation and viscous dissipation in micro-polar nanofluid for MHD stagnation point flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 158-183.
    14. Hsiao, Chun-Hui & Wang, Wen-June, 2001. "Haar wavelet approach to nonlinear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(6), pages 347-353.
    15. Karkera, Harinakshi & Katagi, Nagaraj N. & Kudenatti, Ramesh B., 2020. "Analysis of general unified MHD boundary-layer flow of a viscous fluid - a novel numerical approach through wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 135-154.
    16. C. H. Hsiao & W. J. Wang, 1999. "Optimal Control of Linear Time-Varying Systems via Haar Wavelets," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 641-655, December.
    17. Hsiao, Chun-Hui, 2015. "A Haar wavelets method of solving differential equations characterizing the dynamics of a current collection system for an electric locomotive," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 928-935.
    18. Hsiao, Chun-Hui & Wang, Wen-June, 1999. "State analysis of time-varying singular nonlinear systems via Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 51(1), pages 91-100.
    19. C. H. Hsiao & W. J. Wang, 1999. "State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 623-640, December.
    20. Hsiao, Chun-Hui & Wang, Wen-June, 2000. "State analysis of time-varying singular bilinear systems via Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(1), pages 11-20.

    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:matcom:v:197:y:2022:i:c:p:277-290. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.