IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v333y2018icp213-224.html
   My bibliography  Save this article

Fully discrete spectral methods for solving time fractional nonlinear Sine–Gordon equation with smooth and non-smooth solutions

Author

Listed:
  • Liu, Zeting
  • Lü, Shujuan
  • Liu, Fawang

Abstract

We consider the initial boundary value problem of the time fractional nonlinear Sine–Gordon equation and the fractional derivative is described in Caputo sense with the order α(1 < α < 2). Two fully discrete schemes are developed based on Legendre spectral approximation in space and finite difference discretization in time for smooth solutions and non-smooth solutions, respectively. Numerical stability and convergence are analysed. Numerical experiments for both the fully discrete schemes are presented to confirm our theoretical analysis.

Suggested Citation

  • Liu, Zeting & Lü, Shujuan & Liu, Fawang, 2018. "Fully discrete spectral methods for solving time fractional nonlinear Sine–Gordon equation with smooth and non-smooth solutions," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 213-224.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:213-224
    DOI: 10.1016/j.amc.2018.03.069
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031830242X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.03.069?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. Laskin, N. & Zaslavsky, G., 2006. "Nonlinear fractional dynamics on a lattice with long range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 38-54.
    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. Li, Meng & Fei, Mingfa & Wang, Nan & Huang, Chengming, 2020. "A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 404-419.
    2. Xu, Yibin & Liu, Yanqin & Yin, Xiuling & Feng, Libo & Wang, Zihua & Li, Qiuping, 2023. "A fast time stepping Legendre spectral method for solving fractional Cable equation with smooth and non-smooth solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 154-170.

    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, Chaoxia & Yu, Simin, 2011. "Generation of multi-wing chaotic attractor in fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 845-850.
    2. Tarasov, Vasily E., 2023. "Nonlocal statistical mechanics: General fractional Liouville equations and their solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    3. Tarasov, Vasily E., 2015. "Lattice fractional calculus," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 12-33.
    4. Vasily E. Tarasov, 2024. "Exact Finite-Difference Calculus: Beyond Set of Entire Functions," Mathematics, MDPI, vol. 12(7), pages 1-37, March.
    5. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Taneco-Hernández, M.A., 2018. "Fractional conformable derivatives of Liouville–Caputo type with low-fractionality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 424-438.
    6. Michelitsch, T.M. & Collet, B.A. & Riascos, A.P. & Nowakowski, A.F. & Nicolleau, F.C.G.A., 2016. "A fractional generalization of the classical lattice dynamics approach," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 43-50.
    7. Tarasov, Vasily E., 2015. "Fractional Liouville equation on lattice phase-space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 330-342.
    8. Ishiwata, Ryosuke & Sugiyama, Yūki, 2012. "Relationships between power-law long-range interactions and fractional mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5827-5838.
    9. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 293-310.
    10. Tarasov, Vasily E. & Zaslavsky, George M., 2007. "Fractional dynamics of systems with long-range space interaction and temporal memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 291-308.

    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:333:y:2018:i:c:p:213-224. 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.