Convergence of an energy-conserving scheme for nonlinear space fractional Schrödinger equations with wave operator

Abstract

This paper focuses on the construction and analysis of the energy-conserving numerical schemes for the generalized nonlinear space fractional Schrödinger equations with wave operator. Combining the scalar auxiliary variable (SAV) approach, we present an energy-conserving and linearly implicit scheme, while the previous conservative schemes are generally fully implicit. The energy-conserving property, boundedness and convergence of the numerical solution of the fully discrete scheme are derived for one and multi-dimensional cases. The numerical analysis is also considered. Finally, numerical examples on several fractional models illustrate that the proposed scheme can guarantee conservation of the system energy and confirm our theoretical results.