A high-order structure-preserving difference scheme for generalized fractional Schrödinger equation with wave operator

Abstract

This paper focuses on the construction and analysis of the structure-preserving algorithm for generalized fractional Schrödinger equation with wave operator. A fourth-order energy-conserving difference scheme is developed for the resulting equivalent system based on scalar auxiliary variable approach. The discrete energy conservation law, boundedness and convergence of difference solutions are proved in detail. Numerical experiments are performed to verify our theoretical analysis results.