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This paper uses the finite difference method to numerically solve the space fractional nonlinear Schrodinger equation. First, we give some properties of the fractional Laplacian $Δ_h^\alpha.$ Then we construct a numerical scheme which satisfies the mass conservation law without proof and the scheme’s order is $o(\tau^2+h^2)$ in the discrete $L^\infty$ norm. Moreover, The scheme conserves the mass conservation and is unconditionally stable about the initial values. Finally, this article gives a numerical example to verify the relevant properties of the scheme.
}, issn = {1746-7659}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22370.html} }This paper uses the finite difference method to numerically solve the space fractional nonlinear Schrodinger equation. First, we give some properties of the fractional Laplacian $Δ_h^\alpha.$ Then we construct a numerical scheme which satisfies the mass conservation law without proof and the scheme’s order is $o(\tau^2+h^2)$ in the discrete $L^\infty$ norm. Moreover, The scheme conserves the mass conservation and is unconditionally stable about the initial values. Finally, this article gives a numerical example to verify the relevant properties of the scheme.