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A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative

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  • M. Taghipour
  • H. Aminikhah

Abstract

In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have been approximated by first and second derivatives of the cubic B-spline quasi-interpolation. The discrete scheme obtained in this way constitutes a system of algebraic equations associated with a bi-pentadiagonal matrix. We show that the proposed scheme is unconditionally stable. Numerical examples are provided to verify the efficiency of the method.

Suggested Citation

  • M. Taghipour & H. Aminikhah, 2021. "A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-14, January.
    • Handle: RePEc:hin:jnlmpe:8837846
    DOI: 10.1155/2021/8837846
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