Numerical solutions of nonlinear fractional Schrödinger equations using nonstandard discretizations |
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Authors: | Nasser H. Sweilam Taghreed A. Assiri Muner M. Abou Hasan |
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Affiliation: | 1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt;2. Department of Mathematics, Faculty of Science, Um‐Alqura University, Saudi Arabia |
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Abstract: | In this article, numerical study for both nonlinear space‐fractional Schrödinger equation and the coupled nonlinear space‐fractional Schrödinger system is presented. We offer here the weighted average nonstandard finite difference method (WANSFDM) as a novel numerical technique to study such kinds of partial differential equations. The space fractional derivative is described in the sense of the quantum Riesz‐Feller definition. Stability analysis of the proposed method is studied. To show that this method is reliable and computationally efficient different numerical examples are provided. We expect that the proposed schemes can be applicable to different systems of fractional partial differential equations. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1399–1419, 2017 |
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Keywords: | nonlinear fractional Schrö dinger equation quantum Riesz‐Feller fractional definition weighted average nonstandard finite difference method |
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