IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v290y2016icp111-124.html
   My bibliography  Save this article

An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers’ equation

Author

Listed:
  • Tamsir, Mohammad
  • Srivastava, Vineet K.
  • Jiwari, Ram

Abstract

In this paper, the authors developed a new differential quadrature method "exponential modified cubic B-spline differential quadrature method (Expo-MCB-DQM)” by using exponential modified cubic B-spline functions as test functions in the traditional differential quadrature method [32]. The new method is tested on one and two dimensional nonlinear Burgers’ equations. To check the efficiency and accuracy of the proposed method five numerical problems have been considered. The numerical results of the method are compared with some existing methods and found that the proposed numerical method produces more accurate results than existing methods. Stability analysis of the algorithm is also done by using matrix stability analysis method.

Suggested Citation

  • Tamsir, Mohammad & Srivastava, Vineet K. & Jiwari, Ram, 2016. "An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 111-124.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:111-124
    DOI: 10.1016/j.amc.2016.05.048
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316303642
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.05.048?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. Saka, Bülent & Dağ, İdris, 2007. "Quartic B-spline collocation method to the numerical solutions of the Burgers’ equation," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1125-1137.
    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. Richa Rani & Geeta Arora, 2024. "A Comparative Study of PSO and LOOCV for the Numerical Approximation of Sine–Gordon Equation with Exponential Modified Cubic B-Spline DQM," SN Operations Research Forum, Springer, vol. 5(4), pages 1-31, December.
    2. Kaur, Navneet & Joshi, Varun, 2024. "Kuramoto-Sivashinsky equation: Numerical solution using two quintic B-splines and differential quadrature method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 105-127.
    3. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    4. Chen, Changkai & Zhang, Xiaohua & Liu, Zhang, 2020. "A high-order compact finite difference scheme and precise integration method based on modified Hopf-Cole transformation for numerical simulation of n-dimensional Burgers’ system," Applied Mathematics and Computation, Elsevier, vol. 372(C).

    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. Lin, Bin & Li, Kaitai & Cheng, Zhengxing, 2009. "B-spline solution of a singularly perturbed boundary value problem arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2934-2948.
    2. Jiwari, Ram, 2022. "Local radial basis function-finite difference based algorithms for singularly perturbed Burgers’ model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 106-126.
    3. Rawani, Mukesh Kumar & Verma, Amit Kumar & Verma, Lajja, 2024. "Numerical treatment of Burgers' equation based on weakly L-stable generalized time integration formula with the NSFD scheme," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    4. Singh, Brajesh Kumar & Gupta, Mukesh, 2021. "A new efficient fourth order collocation scheme for solving Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 399(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:290:y:2016:i:c:p:111-124. 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.