Optimal l∞ error estimates of the conservative scheme for two-dimensional Schrödinger equations with wave operator

Abstract

In this work, we consider the numerical computation for the two-dimensional generalized nonlinear Schrödinger equations with wave operator. Based on the scalar auxiliary variable (SAV) approach, the original problem is transformed into an equivalent one, which corresponds to the energy-conservation laws. We present an energy-conserving and linearly implicit three-level scheme for the equivalent system. The energy-conserving property, boundedness of the numerical solution and convergence analysis in the discrete maximum norm are derived, which has not restricted to specific forms of cubic nonlinear term f and not needed the sharply restriction on mesh size. Finally, numerical experiments on several models confirm our theoretical results.