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A numerical solution of the Burgers’ equation using septic B-splines

Author

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  • Ramadan, Mohamed A.
  • El-Danaf, Talaat S.
  • Abd Alaal, Faisal E.I.

Abstract

In this paper, numerical solutions of the nonlinear Burgers’ equation are obtained by a method based on collocation of septic B-splines over finite elements. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Numerical solutions of the modified Burgers’ equation are also obtained by making a simple change of the suggested numerical scheme for the Burgers’ equation. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:3:p:795-804
    DOI: 10.1016/j.chaos.2005.01.054
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    Cited by:

    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.
    2. 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.
    3. Chen, Hao & Nikan, Omid & Qiu, Wenlin & Avazzadeh, Zakieh, 2023. "Two-grid finite difference method for 1D fourth-order Sobolev-type equation with Burgers’ type nonlinearity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 248-266.

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