IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v215y2024icp43-68.html
   My bibliography  Save this article

A robust higher-order finite difference technique for a time-fractional singularly perturbed problem

Author

Listed:
  • Sahoo, Sanjay Ku
  • Gupta, Vikas
  • Dubey, Shruti

Abstract

A higher-order finite difference method is developed to solve the variable coefficients convection–diffusion singularly perturbed problems (SPPs) involving fractional-order time derivative with the order α∈(0,1). The solution to this problem class possesses a typical weak singularity at the initial time t=0 and an exponential boundary layer at the right lateral surface as the perturbation parameter ɛ→0. Alikhanov’s L2−1σ approximation is applied in the temporal direction on a suitable graded mesh, and the spatial variable is discretized on a piecewise uniform Shishkin mesh using a combination of midpoint upwind and central finite difference operators. Stability estimates and the convergence analysis of the fully discrete scheme are provided. It is shown that the fully discrete scheme is uniformly convergent with a rate of O(M−p+N−2(logN)2), where p=min{2,rα}, r is the graded mesh parameter and M,N are the number of mesh points in the time and space direction, respectively. Two numerical examples are taken in counter to confirm the sharpness of the theoretical estimates.

Suggested Citation

  • Sahoo, Sanjay Ku & Gupta, Vikas & Dubey, Shruti, 2024. "A robust higher-order finite difference technique for a time-fractional singularly perturbed problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 43-68.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:43-68
    DOI: 10.1016/j.matcom.2023.08.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423003397
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.08.013?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. Clavero, C. & Vigo-Aguiar, J., 2018. "Numerical approximation of 2D time dependent singularly perturbed convection–diffusion problems with attractive or repulsive turning points," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 223-233.
    2. Abdon Atangana & Emile Franc Doungmo Goufo, 2014. "Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, November.
    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. Zhengang Zhao & Yunying Zheng, 2024. "Galerkin Finite Element Method for Caputo–Hadamard Time-Space Fractional Diffusion Equation," Mathematics, MDPI, vol. 12(23), pages 1-14, November.

    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. Uddin, M. Hafiz & Zaman, U.H.M. & Arefin, Mohammad Asif & Akbar, M. Ali, 2022. "Nonlinear dispersive wave propagation pattern in optical fiber system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Panda, Sumati Kumari & Ravichandran, C. & Hazarika, Bipan, 2021. "Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Dubey, Shweta & Chakraverty, S., 2022. "Application of modified extended tanh method in solving fractional order coupled wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 509-520.
    4. Akram, Ghazala & Sadaf, Maasoomah & Abbas, Muhammad & Zainab, Iqra & Gillani, Syeda Rijaa, 2022. "Efficient techniques for traveling wave solutions of time-fractional Zakharov–Kuznetsov equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 607-622.
    5. Yadav, Swati & Rai, Pratima, 2023. "A parameter uniform higher order scheme for 2D singularly perturbed parabolic convection–diffusion problem with turning point," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 507-531.

    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:43-68. 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.