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Quartic B-spline collocation method to the numerical solutions of the Burgers’ equation

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  • Saka, Bülent
  • Dağ, İdris

Abstract

The collocation method using quartic B-splines is described for the numerical solutions of the Burgers’ equation. The effect of the quartic B-splines in the collocation method is sought. The same method is applied to the time split Burgers’ equation. Numerical comparison of results of both algorithms and some other published numerical results are done by studying three standard problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:3:p:1125-1137
    DOI: 10.1016/j.chaos.2005.11.037
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    References listed on IDEAS

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    1. Ramadan, Mohamed A. & El-Danaf, Talaat S. & Abd Alaal, Faisal E.I., 2005. "A numerical solution of the Burgers’ equation using septic B-splines," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 795-804.
    2. Ramadan, Mohamed A. & El-Danaf, Talaat S. & Abd Alaal, Faisal E.I., 2005. "A numerical solution of the Burgers’ equation using septic B-splines," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1249-1258.
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    Cited by:

    1. 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.
    2. 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).
    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. 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.
    5. 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.

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