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Numerical solutions of nonlinear fractional Schrödinger equations using nonstandard discretizations
Author(s) -
Sweilam Nasser H.,
Assiri Taghreed A.,
Abou Hasan Muner M.
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22117
Subject(s) - mathematics , fractional calculus , nonlinear system , partial differential equation , partial derivative , space (punctuation) , stability (learning theory) , mathematical analysis , numerical analysis , physics , quantum mechanics , machine learning , computer science , linguistics , philosophy
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