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

This paper focuses on the construction and analysis of the energy-conserving numerical schemes for the generalized nonlinear space fractional Schrodinger 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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper focuses on the construction and analysis of energy-conserving numerical schemes for generalized nonlinear space fractional Schrodinger equations with wave operator. An energy-conserving and linearly implicit scheme is presented, and numerical examples confirm the effectiveness of the proposed scheme in conserving system energy.