IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v545y2020ics0378437119320837.html
   My bibliography  Save this article

Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations

Author

Listed:
  • Pervaiz, Nosheen
  • Aziz, Imran

Abstract

In this study, Haar wavelet collocation method is used for the numerical solution of 1D and 2D cubic nonlinear Schrodinger equations with initial and Dirichlet boundary conditions. The space derivatives are estimated through Haar wavelet collocation method whereas for time derivative we have used Crank–Nicolson scheme. The proposed method is implemented upon several test problems and the numerical results of these test problems establish that the proposed method is accurate.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320837
    DOI: 10.1016/j.physa.2019.123738
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119320837
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123738?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. 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.
    2. 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.
    3. Hsiao, C.H., 2004. "Haar wavelet approach to linear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 561-567.
    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. 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.
    2. Rawani, Mukesh Kumar & Verma, Amit Kumar & Verma, Lajja, 2024. "Numerical treatment of Burgers' equation based on weakly L-stable generalized time integration formula with the NSFD scheme," Applied Mathematics and Computation, Elsevier, vol. 467(C).

    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. Siraj-ul-Islam, & Haider, Nadeem & Aziz, Imran, 2018. "Meshless and multi-resolution collocation techniques for parabolic interface models," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 313-332.
    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. Tian, Yongge & Herzberg, Agnes M., 2006. "A-minimax and D-minimax robust optimal designs for approximately linear Haar-wavelet models," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2942-2951, June.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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. Usman, Muhammad & Hamid, Muhammad & Liu, Moubin, 2021. "Novel operational matrices-based finite difference/spectral algorithm for a class of time-fractional Burger equation in multidimensions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    11. 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.
    12. Karabulut, Gokhan & Bilgin, Mehmet Huseyin & Doker, Asli Cansin, 2020. "The relationship between commodity prices and world trade uncertainty," Economic Analysis and Policy, Elsevier, vol. 66(C), pages 276-281.
    13. 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.
    14. 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.
    15. Lepik, Ü., 2005. "Numerical solution of differential equations using Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 127-143.
    16. 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.
    17. Li, Jiyong, 2021. "Convergence analysis of a symmetric exponential integrator Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 691-713.
    18. 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.
    19. Mohammad, Mutaz & Trounev, Alexander, 2020. "Implicit Riesz wavelets based-method for solving singular fractional integro-differential equations with applications to hematopoietic stem cell modeling," Chaos, Solitons & Fractals, Elsevier, vol. 138(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:phsmap:v:545:y:2020:i:c:s0378437119320837. 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/physica-a-statistical-mechpplications/ .

    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.