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A fourth-order difference scheme for the fractional nonlinear Schrödinger equation with wave operator
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-10-13 , DOI: 10.1080/00036811.2020.1829600 Kejia Pan 1 , Jiali Zeng 1 , Dongdong He 2 , Saiyan Zhang 1
中文翻译:
带波算子的分数阶非线性薛定谔方程的四阶差分格式
更新日期:2020-10-13
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-10-13 , DOI: 10.1080/00036811.2020.1829600 Kejia Pan 1 , Jiali Zeng 1 , Dongdong He 2 , Saiyan Zhang 1
Affiliation
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.
中文翻译:
带波算子的分数阶非线性薛定谔方程的四阶差分格式
摘要
本文提出并分析了一种有效的半隐式微分格式,用于求解带波算子的分数非线性薛定谔方程。半隐式方案涉及三个时间层次,是无条件稳定的,在空间上是四阶精确的,在时间上是二阶精确的。此外,该方法的独特可解性、无条件稳定性和收敛性-范数由能量方法严格证明。最后,给出了数值实验来证实我们的理论结果。