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

In this work, we consider the numerical computation for the two-dimensional generalized nonlinear Schrodinger 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.

Automated summary

The numerical computation for the two-dimensional generalized nonlinear Schrodinger equations with wave operator is considered in this work. A three-level scheme for the equivalent system is proposed which conserves energy and is linearly implicit. The energy-conserving property, boundedness of the numerical solution and convergence analysis are derived, with numerical experiments confirming the theoretical results.