A Linear Finite Difference Scheme for the Two-Dimensional Nonlinear Schrödinger Equation with Fractional Laplacian

In this paper, we propose a conservative three-layer linearized difference scheme for the two-dimensional nonlinear Schrodinger equation with fractional Laplacian. The difference scheme can be strictly proved to be uniquely solvable, conservation of mass and energy in the discrete sense. Furthermore, it is shown that the difference scheme is unconditionally convergent and stable under $$l^{\infty }$$ -norm by discrete energy method. The convergence order is $$\mathcal {O}(\tau ^2+h^2)$$ with time step $$\tau $$ and mesh size h. Numerical examples are given to demonstrate the theoretical results.