Optimal Pointwise Error Estimate for the Numerical solutions of Two-dimensional Space Fractional Nonlinear Schrödinger Equation
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In this paper, a linearized conservative semi-implicit finite difference scheme is proposed for the two-dimensional (2D) space fractional nonlinear Schrödinger equation (SFNSE). The scheme involves three-time levels, is unconditionally stable and second-order accurate both in time and space variables. The main contribution of this paper is that an optimal pointwise error estimate is first time obtained for the 2D SFNSE. Numerical results are presented to confirm the theoretical findings.
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