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

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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).

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