IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v389y2021ics0096300320305336.html
   My bibliography  Save this article

A pseudospectral method for the one-dimensional fractional Laplacian on R

Author

Listed:
  • Cayama, Jorge
  • Cuesta, Carlota M.
  • de la Hoz, Francisco

Abstract

In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map the unbounded domain into a finite one, and represent the resulting function as a trigonometric series. Therefore, the central point of this paper is the computation of the fractional Laplacian of an elementary trigonometric function.

Suggested Citation

  • Cayama, Jorge & Cuesta, Carlota M. & de la Hoz, Francisco, 2021. "A pseudospectral method for the one-dimensional fractional Laplacian on R," Applied Mathematics and Computation, Elsevier, vol. 389(C).
  • Handle: RePEc:eee:apmaco:v:389:y:2021:i:c:s0096300320305336
    DOI: 10.1016/j.amc.2020.125577
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320305336
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2020.125577?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. Khader, M.M. & Saad, K.M., 2018. "A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 169-177.
    2. Hans Engler, 2010. "On the Speed of Spread for Fractional Reaction-Diffusion Equations," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-16, November.
    3. Olmos, Daniel & Shizgal, Bernie D., 2009. "Pseudospectral method of solution of the Fitzhugh–Nagumo equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2258-2278.
    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. Singh, C.S. & Singh, Harendra & Singh, Somveer & Kumar, Devendra, 2019. "An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1440-1448.
    2. Khader, M.M. & Inc, Mustafa, 2021. "Numerical technique based on the interpolation with Lagrange polynomials to analyze the fractional variable-order mathematical model of the hepatitis C with different types of virus genome," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Haifa Bin Jebreen, 2024. "A Highly Accurate Computational Approach to Solving the Diffusion Equation of a Fractional Order," Mathematics, MDPI, vol. 12(13), pages 1-15, June.
    4. Khater, Mostafa M.A. & Mohamed, Mohamed S. & Attia, Raghda A.M., 2021. "On semi analytical and numerical simulations for a mathematical biological model; the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. H. Çerdik Yaslan, 2021. "Numerical solution of the nonlinear conformable space–time fractional partial differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 407-419, June.
    6. Hari Mohan Srivastava & Khaled M. Saad, 2020. "A Comparative Study of the Fractional-Order Clock Chemical Model," Mathematics, MDPI, vol. 8(9), pages 1-14, August.
    7. Rodríguez-Padilla, Jairo & Olmos-Liceaga, Daniel, 2018. "Numerical solutions of equations of cardiac wave propagation based on Chebyshev multidomain pseudospectral methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 29-53.
    8. Agarwal, P. & Deni̇z, S. & Jain, S. & Alderremy, A.A. & Aly, Shaban, 2020. "A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    9. Saad, Khaled M., 2021. "Fractal-fractional Brusselator chemical reaction," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Maryam Al Owidh & Basma Souayeh & Imran Qasim Memon & Kashif Ali Abro & Huda Alfannakh, 2022. "Heat Transfer and Fluid Circulation of Thermoelectric Fluid through the Fractional Approach Based on Local Kernel," Energies, MDPI, vol. 15(22), pages 1-12, November.
    11. Che, Han & Wang, Yu-Lan & Li, Zhi-Yuan, 2022. "Novel patterns in a class of fractional reaction–diffusion models with the Riesz fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 149-163.
    12. Heydari, M.H. & Razzaghi, M. & Avazzadeh, Z., 2021. "Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrödinger-Boussinesq system," Chaos, Solitons & Fractals, Elsevier, vol. 143(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:apmaco:v:389:y:2021:i:c:s0096300320305336. 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.