IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v215y2024icp382-398.html
   My bibliography  Save this article

A finite difference method on quasi-uniform grids for the fractional boundary-layer Blasius flow

Author

Listed:
  • Jannelli, Alessandra

Abstract

In this paper, we propose a fractional formulation, in terms of the Caputo derivative, of the Blasius flow described by a non-linear two-point fractional boundary value problem on a semi-infinite interval. We develop a finite difference method on quasi-uniform grids, based on a suitable modification of the classical L1 approximation formula and show the consistency, the stability and the convergence. The numerical results confirm the theoretical ones. Comparisons with some recently proposed results are carried out to validate the accuracy of the obtained numerical results, and to show the efficiency and the reliability of the proposed numerical method.

Suggested Citation

  • Jannelli, Alessandra, 2024. "A finite difference method on quasi-uniform grids for the fractional boundary-layer Blasius flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 382-398.
  • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:382-398
    DOI: 10.1016/j.matcom.2023.08.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542300349X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2023.08.023?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. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
    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. Alessandra Jannelli & Maria Paola Speciale, 2024. "Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution," Mathematics, MDPI, vol. 12(2), pages 1-10, January.

    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. Arenas, Abraham J. & González-Parra, Gilberto & Chen-Charpentier, Benito M., 2016. "Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 48-63.
    2. Dmytro Sytnyk & Barbara Wohlmuth, 2023. "Exponentially Convergent Numerical Method for Abstract Cauchy Problem with Fractional Derivative of Caputo Type," Mathematics, MDPI, vol. 11(10), pages 1-35, May.
    3. Wang, Yuan-Ming & Xie, Bo, 2023. "A fourth-order fractional Adams-type implicit–explicit method for nonlinear fractional ordinary differential equations with weakly singular solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 21-48.
    4. Rainey Lyons & Aghalaya S. Vatsala & Ross A. Chiquet, 2017. "Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results," Mathematics, MDPI, vol. 5(4), pages 1-9, November.
    5. Yang, Changqing, 2023. "Improved spectral deferred correction methods for fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    6. Roberto Garrappa, 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial," Mathematics, MDPI, vol. 6(2), pages 1-23, January.
    7. Kai Diethelm & Roberto Garrappa & Martin Stynes, 2020. "Good (and Not So Good) Practices in Computational Methods for Fractional Calculus," Mathematics, MDPI, vol. 8(3), pages 1-21, March.
    8. Cardone, Angelamaria & Conte, Dajana, 2020. "Stability analysis of spline collocation methods for fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 501-514.
    9. Moustafa, Mahmoud & Mohd, Mohd Hafiz & Ismail, Ahmad Izani & Abdullah, Farah Aini, 2018. "Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 1-13.
    10. Das, Saptarshi & Pan, Indranil & Das, Shantanu, 2016. "Effect of random parameter switching on commensurate fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 157-173.
    11. Hamdan, Nur ’Izzati & Kilicman, Adem, 2018. "A fractional order SIR epidemic model for dengue transmission," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 55-62.
    12. Čermák, Jan & Nechvátal, Luděk, 2019. "Stability and chaos in the fractional Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 24-33.
    13. Bonab, Zahra Farzaneh & Javidi, Mohammad, 2020. "Higher order methods for fractional differential equation based on fractional backward differentiation formula of order three," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 71-89.
    14. Sowa, Marcin, 2018. "Application of SubIval in solving initial value problems with fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 86-103.
    15. Marina Popolizio, 2018. "Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions," Mathematics, MDPI, vol. 6(1), pages 1-13, January.

    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:215:y:2024:i:c:p:382-398. 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.