Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrodinger equation with cubic nonlinearity

被引：4

作者：

Yang, Huaijun ^{[1
]}

机构：

[1] Zhengzhou Univ Aeronaut, Sch Math, Zhengzhou 450046, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2023年 / 183卷

基金：

中国国家自然科学基金;

关键词：

Cubic Schr?dinger equation; Backward Euler scheme; A modified Crank-Nicolson scheme; Unconditionally optimal error estimate; FINITE-ELEMENT-METHOD; SUPERCONVERGENCE ANALYSIS; DIFFERENCE-SCHEMES; NUMERICAL-SOLUTION; CONVERGENCE; APPROXIMATIONS; FEMS;

D O I：

10.1016/j.apnum.2022.08.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, unconditionally optimal error estimates in L-2-norm of two fully discrete schemes, one is backward Euler scheme and the other is a modified Crank-Nicolson scheme, are derived for cubic Schrodinger equation. Firstly, the mass and energy stability of the two schemes are proved rigorously. Secondly, the existence and uniqueness of the numerical solutions of the two schemes are presented. Based on the above priori estimations of the numerical solutions, unconditionally optimal error estimates in L-2-norm are obtained without any timestep restrictions. Finally, some numerical results are provided to confirm the theoretical analysis. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：39 / 55

页数：17

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