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Numerical solutions for 2-D fractional Schrödinger equation with the Riesz–Feller derivative

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  • Sweilam, N.H.
  • Abou Hasan, M.M.

Abstract

In this paper, we present an accurate numerical method for solving a space-fractional Schrödinger equation in two dimensions. The quantum Riesz–Feller fractional derivative is used to define the fractional derivatives. The weighted average non-standard finite difference method is implemented to study the behavior of the model problem. The stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis; moreover the truncation error is analyzed. Some numerical test examples are presented with variety values of derivatives of order α,where 1<α≤2 and of skewness θ. Experimental findings indicate that the proposed method is easy to implement, effective and convenient for solving the proposed model.

Suggested Citation

  • Sweilam, N.H. & Abou Hasan, M.M., 2017. "Numerical solutions for 2-D fractional Schrödinger equation with the Riesz–Feller derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 140(C), pages 53-68.
    • Handle: RePEc:eee:matcom:v:140:y:2017:i:c:p:53-68
    DOI: 10.1016/j.matcom.2017.02.006
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    Cited by:

    1. Heydari, M.H. & Atangana, A., 2019. "A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana–Baleanu–Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 339-348.

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