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Numerical Simulation and Dynamics of Burgers’ Equation Using the Modified Cubic B-Spline Differential Quadrature Method

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  • Geeta Arora
  • Shubham Mishra
  • Homan Emaifar
  • Masoumeh Khademi
  • Mehmet Emir Koksal

Abstract

In the present work, a numerical approach using the Crank–Nicolson scheme along with the modified cubic B-spline differential quadrature (CN-MCDQ) method is proposed to find the numerical approximations to Burgers’ equation. After applying the well-known Crank–Nicolson technique, Burgers’ equation is solved in this study by using the differential quadrature approach to approximate the derivatives that lead to a system of equations to be solved. When compared to other methods for obtaining numerical solutions, the proposed method is shown to be efficient and easy to implement while still providing accurate results. The obtained results are in agreement with the earlier available approaches and are even better in comparison in terms of less domain partition. Three test problems were used to evaluate the methodology, and the results are tabulated and graphically shown below.

Suggested Citation

  • Geeta Arora & Shubham Mishra & Homan Emaifar & Masoumeh Khademi & Mehmet Emir Koksal, 2023. "Numerical Simulation and Dynamics of Burgers’ Equation Using the Modified Cubic B-Spline Differential Quadrature Method," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-8, March.
    • Handle: RePEc:hin:jnddns:5102374
    DOI: 10.1155/2023/5102374
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