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

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.