IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v431y2022ics0096300322003733.html
   My bibliography  Save this article

Spatiotemporal pattern formations in stiff reaction-diffusion systems by new time marching methods

Author

Listed:
  • Yadav, Vivek S.
  • Maurya, Vikas
  • Rajpoot, Manoj K.
  • Jaglan, Jyoti

Abstract

Reaction-diffusion systems are extensively used in the modeling of developmental biology and in chemical systems to explain the Turing instability are generally highly stiff in both reaction and diffusion terms. For numerical simulations of stiff reaction-diffusion systems, this paper introduces a novel family of implicit-explicit Runge-Kutta (IMEX RK) type methods. Despite being implicit in nature, the developed methods require no numerical or analytical inversion of the coefficient matrix, that is, computationally explicit. Fourier analysis is used to assess the stability results for the developed methods with the model two-dimensional reaction diffusion equation. The efficiency and robustness of the developed methods are validated by numerical simulations of spatiotemporal patterns for reaction-diffusion systems governing phase-separation, the Schnakenberg model, and the electrodeposition process. The results of computed solutions are also compared to those reported in the literature.

Suggested Citation

  • Yadav, Vivek S. & Maurya, Vikas & Rajpoot, Manoj K. & Jaglan, Jyoti, 2022. "Spatiotemporal pattern formations in stiff reaction-diffusion systems by new time marching methods," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322003733
    DOI: 10.1016/j.amc.2022.127299
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322003733
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127299?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. Bozzini, Benedetto & Lacitignola, Deborah & Sgura, Ivonne, 2011. "Travelling waves in a reaction-diffusion model for electrodeposition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1027-1044.
    2. Yadav, Vivek S. & Ganta, Naveen & Mahato, Bikash & Rajpoot, Manoj K. & Bhumkar, Yogesh G., 2022. "New time-marching methods for compressible Navier-Stokes equations with applications to aeroacoustics problems," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    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. Maurya, Vikas & Singh, Ankit & Yadav, Vivek S. & Rajpoot, Manoj K., 2024. "Efficient pricing of options in jump–diffusion models: Novel implicit–explicit methods for numerical valuation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 202-225.

    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:431:y:2022:i:c:s0096300322003733. 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.