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Optimal l∞ error estimates of the conservative scheme for two-dimensional Schrödinger equations with wave operator
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2021-09-10 , DOI: 10.1016/j.camwa.2021.08.026
Xiujun Cheng 1, 2 , Xiaoqiang Yan 3 , Hongyu Qin 4 , Huiru Wang 5
Affiliation  

In this work, we consider the numerical computation for the two-dimensional generalized nonlinear Schrödinger equations with wave operator. Based on the scalar auxiliary variable (SAV) approach, the original problem is transformed into an equivalent one, which corresponds to the energy-conservation laws. We present an energy-conserving and linearly implicit three-level scheme for the equivalent system. The energy-conserving property, boundedness of the numerical solution and convergence analysis in the discrete maximum norm are derived, which has not restricted to specific forms of cubic nonlinear term f and not needed the sharply restriction on mesh size. Finally, numerical experiments on several models confirm our theoretical results.



中文翻译:

带波算子的二维薛定谔方程保守方案的最优 l∞ 误差估计

在这项工作中,我们考虑了具有波算子的二维广义非线性薛定谔方程的数值计算。基于标量辅助变量 (SAV) 方法,将原始问题转化为等效的问题,这对应于能量守恒定律。我们提出了等效系统的节能和线性隐式三级方案。推导了离散最大范数下的能量守恒性质、数值解的有界性和收敛性分析,它不受三次非线性项f的具体形式的限制,也不需要对网格大小进行严格限制。最后,对几个模型的数值实验证实了我们的理论结果。

更新日期:2021-09-10
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