IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v204y2023icp166-180.html
   My bibliography  Save this article

A Haar wavelet multi-resolution collocation method for singularly perturbed differential equations with integral boundary conditions

Author

Listed:
  • Ahsan, Muhammad
  • Bohner, Martin
  • Ullah, Aizaz
  • Khan, Amir Ali
  • Ahmad, Sheraz

Abstract

The focus of this paper is to develop and improve a higher-order Haar wavelet approach for solving nonlinear singularly perturbed differential equations with various pairs of boundary conditions like initial, boundary, two points, integral and multi-point integral boundary conditions. The theoretical convergence and computational stability of the method is also presented. The comparison of the proposed higher-order Haar wavelet method is performed with the recent published work including the well-known Haar wavelet method in terms of convergence and accuracy. In the nonlinear case, a quasilinearization technique has been adopted. The proposed method is easy to implement on various boundary conditions, and the computed results are high-order accurate, stable and efficient. We have also checked the satisfactory performance of the proposed method for nonlinear differential equations having no analytical solution in some of the test problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:166-180
    DOI: 10.1016/j.matcom.2022.08.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422003366
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.08.004?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. Ahsan, Muhammad & Ahmad, Imtiaz & Ahmad, Masood & Hussian, Iltaf, 2019. "A numerical Haar wavelet-finite difference hybrid method for linear and non-linear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 13-25.
    3. 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.
    4. Surla, K. & Uzelac, Z. & Teofanov, Lj., 2009. "The discrete minimum principle for quadratic spline discretization of a singularly perturbed problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2490-2505.
    5. Xuan Liu & Muhammad Ahsan & Masood Ahmad & Muhammad Nisar & Xiaoling Liu & Imtiaz Ahmad & Hijaz Ahmad, 2021. "Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schr ö dinger Equation with Energy and Mass Conversion," Energies, MDPI, vol. 14(23), pages 1-17, November.
    6. Nazir, Shah & Shahzad, Sara & Wirza, Rahmita & Amin, Rohul & Ahsan, Muhammad & Mukhtar, Neelam & García-Magariño, Iván & Lloret, Jaime, 2019. "Birthmark based identification of software piracy using Haar wavelet," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 144-154.
    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. Ahsan, Muhammad & Lei, Weidong & Bohner, Martin & Khan, Amir Ali, 2024. "A high-order multi-resolution wavelet method for nonlinear systems of differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 543-559.

    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. Ahsan, Muhammad & Lei, Weidong & Bohner, Martin & Khan, Amir Ali, 2024. "A high-order multi-resolution wavelet method for nonlinear systems of differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 543-559.
    2. Xuan Liu & Muhammad Ahsan & Masood Ahmad & Muhammad Nisar & Xiaoling Liu & Imtiaz Ahmad & Hijaz Ahmad, 2021. "Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schr ö dinger Equation with Energy and Mass Conversion," Energies, MDPI, vol. 14(23), pages 1-17, November.
    3. 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.
    4. Xiaofei Qin & Youhua Fan & Hongjun Li & Weidong Lei, 2022. "A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics," Mathematics, MDPI, vol. 10(2), pages 1-17, January.
    5. Khater, Mostafa M.A., 2023. "Computational simulations of propagation of a tsunami wave across the ocean," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. 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.
    7. Singh, Randhir & Guleria, Vandana & Singh, Mehakpreet, 2020. "Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 123-133.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Amin, Rohul & Shah, Kamal & Asif, Muhammad & Khan, Imran, 2021. "A computational algorithm for the numerical solution of fractional order delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    15. 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.
    16. Toprakseven, Şuayip & Zhu, Peng, 2023. "Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms," Applied Mathematics and Computation, Elsevier, vol. 441(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:eee:matcom:v:204:y:2023:i:c:p:166-180. 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.