立方Schr?dinger方程的半隐格式BDF2-FEM无条件最优误差估计  

Unconditionally Optimal Error Estimates of the Semi-Implicit BDF2-FEM for Cubic Schr?dinger Equations

作　　者：代猛 尹小艳 DAI Meng;YIN Xiaoyan(School of Mathematics and Statistics,Xidian University,Xi’an 710071,P.R.China)

机构地区：[1]西安电子科技大学数学与统计学院

出　　处：《应用数学和力学》2019年第6期663-681,共19页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(面上项目)(11771259);中央高校基础科研业务费(JB180714)~~

摘　　要：研究了立方Schrodinger方程的二阶向后差分有限元方法(BDF2-FEM)的无条件最优误差估计.首先,将误差分为时间误差和空间误差两部分.通过引入时间离散方程,得到时间离散方程解的一致有界性,并给出时间误差估计.从而得到该方程在半隐格式下BDF2-FEM无条件最优误差估计.最后,用数值算例验证了理论分析.The optimal error estimates of the semi-implicit BDF2-FEM were studied for cubic Schrodinger equations.First,an error estimate was divided into 2 parts:the temporal-discretization and the spatial-discretization.Through introduction of a temporal-discretization equation,the uniform boundedness of the solution and the temporal error estimate were obtained.The unconditionally optimal error estimates of the 2nd-order backward difference(BDF2-FEM)semi-implicit scheme for cubic Schr dinger equations were given.Finally,numerical examples verify the theoretical analysis.

关 键 词：无条件收敛 向后Euler法 GALERKIN有限元方法 SCHRODINGER方程 

分 类 号：O241.82[理学—计算数学]