A fourth-order difference scheme for the fractional nonlinear Schrödinger equation with wave operator. Issue 8 (24th May 2022) - Pan, Kejia; Zeng, Jiali; He, Dongdong; Zhang, Saiyan
ABSTRACT: In this paper, an efficient semi-implicit difference scheme for solving the fractional nonlinear Schrödinger equation with wave operator are proposed and analyzed. The semi-implicit scheme involves three-time levels, is unconditionally stable and fourth-order accurate in space and second-order accurate in time. Furthermore, the unique solvability, unconditional stability and convergence of the method in the L ∞ -norm are proved rigorously by the energy method. Finally, numerical experiments are presented to confirm our theoretical results.