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An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis

Author

Listed:
  • N. Abdi
  • H. Aminikhah
  • A. H. Refahi Sheikhani
  • J. Alavi
  • M. Taghipour

Abstract

In this paper, the Crank–Nicolson (CN) and rotated four‐point fractional explicit decoupled group (EDG) methods are introduced to solve the two‐dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the x and y axes. The local truncation error of CN and EDG is presented. Also, the stability and convergence of the proposed methods are proved. Some numerical experiments are performed to show the efficiency of the presented methods in terms of accuracy and CPU time.

Suggested Citation

  • N. Abdi & H. Aminikhah & A. H. Refahi Sheikhani & J. Alavi & M. Taghipour, 2021. "An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6669287
    DOI: 10.1155/2021/6669287
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    References listed on IDEAS

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    1. Liu, Zhengguang & Cheng, Aijie & Li, Xiaoli, 2017. "A second order Crank–Nicolson scheme for fractional Cattaneo equation based on new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 361-374.
    2. Kong, Desong & Xu, Yufeng & Zheng, Zhoushun, 2019. "A hybrid numerical method for the KdV equation by finite difference and sinc collocation method," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 61-72.
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