IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v297y2017icp131-144.html
   My bibliography  Save this article

An efficient time-splitting compact finite difference method for Gross–Pitaevskii equation

Author

Listed:
  • Wang, Hanquan
  • Ma, Xiu
  • Lu, Junliang
  • Gao, Wen

Abstract

We propose an efficient time-splitting compact finite difference method for Gross–Pitaevskii equation (GPE). In our method, we solve the GPE in time with time-splitting technique and in space by the compact finite difference method. To find the numerical solution of the resulting discretized system in one-dimension (1D), two-dimensions (2D) and three-dimensions (3D), we apply the fast discrete Sine transform in 1D, 2D and 3D respectively and get an efficient solver for the discretized system in 1D, 2D and 3D, respectively. Our numerical algorithm at every time step does not need linear-algebraic-equations-solver, whose computation cost will be much higher when the spatial dimension increases. The method also has the merit that it is unconditionally stable and conservative. Moreover the method can achieve spectral-like accuracy in space when high-order compact finite difference method is applied. Extensive numerical tests for the GPE in 1D, 2D and 3D are presented to demonstrate the power and accuracy of the proposed numerical method.

Suggested Citation

  • Wang, Hanquan & Ma, Xiu & Lu, Junliang & Gao, Wen, 2017. "An efficient time-splitting compact finite difference method for Gross–Pitaevskii equation," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 131-144.
    • Handle: RePEc:eee:apmaco:v:297:y:2017:i:c:p:131-144
    DOI: 10.1016/j.amc.2016.10.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316306440
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.10.037?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. Dehghan, Mehdi, 2006. "Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(1), pages 16-30.
    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. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 240-248.
    2. Ghosh, Suchismita & Deb, Anish & Sarkar, Gautam, 2016. "Taylor series approach for function approximation using ‘estimated’ higher derivatives," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 89-101.
    3. Guo, Geyang & Lü, Shujuan & Liu, Bo, 2015. "Unconditional stability of alternating difference schemes with variable time steplengthes for dispersive equation," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 249-259.
    4. Mohammadi, Reza, 2018. "Smooth Quintic spline approximation for nonlinear Schrödinger equations with variable coefficients in one and two dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 204-215.
    5. Dehghan, Mehdi & Mohebbi, Akbar, 2008. "High-order compact boundary value method for the solution of unsteady convection–diffusion problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 683-699.
    6. Dehghan, Mehdi & Gharibi, Zeinab, 2021. "Numerical analysis of fully discrete energy stable weak Galerkin finite element Scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    7. Nehad Ali Shah & Ioannis Dassios & Essam R. El-Zahar & Jae Dong Chung & Somaye Taherifar, 2021. "The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method," Mathematics, MDPI, vol. 9(2), pages 1-14, January.
    8. 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.
    9. Kaur, Navneet & Joshi, Varun, 2024. "Kuramoto-Sivashinsky equation: Numerical solution using two quintic B-splines and differential quadrature method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 105-127.
    10. Luo, Yidong, 2020. "Galerkin method with trigonometric basis on stable numerical differentiation," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    11. Dehghan, Mehdi & Saadatmandi, Abbas, 2009. "Variational iteration method for solving the wave equation subject to an integral conservation condition," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1448-1453.
    12. Dehghan, Mehdi & Shokri, Ali, 2008. "A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 700-715.
    13. Kenzu Abdella & Jeet Trivedi, 2020. "Solving Multi-Point Boundary Value Problems Using Sinc-Derivative Interpolation," Mathematics, MDPI, vol. 8(12), pages 1-14, November.
    14. Shi, Dongyang & Liao, Xin & Wang, Lele, 2016. "Superconvergence analysis of conforming finite element method for nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 298-310.
    15. Gao, Yali & Mei, Liquan & Li, Rui, 2018. "Galerkin methods for the Davey–Stewartson equations," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 144-161.

    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:apmaco:v:297:y:2017:i:c:p:131-144. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.