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Numerical Studies for the Fractional Schrodinger Equation with the Quantum Riesz-Feller Derivative |
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PP: 231-245 |
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doi:10.18576/pfda/020401
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Author(s) |
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Nasser Hassan Sweilam,
Muner Mustafa Abou Hasan,
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Abstract |
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| In this paper, we present a numerical method for solving the one-dimensional space fractional Schršodinger equation in the
case of a particle moving in a potential field. The fractional derivative is defined by the quantum Riesz-Feller fractional derivative. A
novel weighted average non-standard finite difference method is presented to solve the underline problem numerically. The stability
analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis
and the truncation error is analyzed. Several numerical examples are introduced for various choices of derivative order a, 1
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