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<p>The nonlinear Burgers equation as a partial differential equation occurs in most physical and mathematical fields such as traffic flow. The equation is extracted from the Navier–Stokes equation by omission of the pressure terms. The effects of two topics are combined with Burgers equation as the diffusive and nonlinear effects. In the present study, using Crank–Nicholson finite difference technique such a problem is handled and the fractional derivative is approximated using the fractional Caputo-Fabrizio derivative. Convergence and stability are examined. Thus, the suggested scheme is stable unconditionally and includes first and second-order accuracy in time and space. A comparison was made between the numerical results with those of exact solutions.</p>

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Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月14日

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  • L. Azami,
  • A. H. Refahi Sheikhani,
  • H. Saberi Najafi

摘要

The nonlinear Burgers equation as a partial differential equation occurs in most physical and mathematical fields such as traffic flow. The equation is extracted from the Navier–Stokes equation by omission of the pressure terms. The effects of two topics are combined with Burgers equation as the diffusive and nonlinear effects. In the present study, using Crank–Nicholson finite difference technique such a problem is handled and the fractional derivative is approximated using the fractional Caputo-Fabrizio derivative. Convergence and stability are examined. Thus, the suggested scheme is stable unconditionally and includes first and second-order accuracy in time and space. A comparison was made between the numerical results with those of exact solutions.