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

N.H. Sweilam and M.M. Abou Hasan

Mathematics and Computers in Simulation (MATCOM), 2017, vol. 140, issue C, 53-68

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.

Keywords: Two-dimensional space-fractional Schrödinger equation; Quantum Riesz–Feller operator; Weighted average non-standard finite difference method; John von Neumann stability analysis (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:140:y:2017:i:c:p:53-68

DOI: 10.1016/j.matcom.2017.02.006

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