Improved Mass- and Energy-Conserving Difference Scheme for Two-Dimensional Nonlinear Space-Fractional Schrödinger Equation
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In this paper, we focus on develop high-order and structure-preserving numerical algorithm for the two-dimensional nonlinear space fractional Schr\"{o}dinger equations. By using the scalar auxiliary variable method with the composite Simpson's formula, and a fourth-order numerical differential formula for Riesz derivative, an effective difference scheme is constructed. Meanwhile, the conserving properties of the numerical solution is also studied.