ABSTRACT
In this paper, an efficient semi-implicit difference scheme for solving the fractional nonlinear Schrödinger equation with wave operator are proposed and analyzed. The semi-implicit scheme involves three-time levels, is unconditionally stable and fourth-order accurate in space and second-order accurate in time. Furthermore, the unique solvability, unconditional stability and convergence of the method in the -norm are proved rigorously by the energy method. Finally, numerical experiments are presented to confirm our theoretical results.
2010 Mathematics Subject Classification:
Acknowledgments
The authors would like to thank the two anonymous referees for valuable suggestions, which helped to improve the quality of the paper. Kejia Pan was supported by Science Challenge Project (No. TZ2016002), the National Natural Science Foundation of China (No. 41874086), the Excellent Youth Foundation of Hunan Province of China (No. 2018JJ1042). Dongdong He was supported by the president's fund-research start-up fund from the Chinese University of Hong Kong, Shenzhen (No. PF01000857).
Disclosure statement
No potential conflict of interest was reported by the author(s).