薛定谔方程的虚拟元分析

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Abstract

本文旨在研究基于虚拟元方法的非线性Schrödinger方程(NLSW)的数值求解,该方程包含波动算子.首先,利用误差分裂技术将时空误差分解为时间误差和空间误差.其次,使用截断函数方法处理非线性项.误差分裂技术和截断函数方法在时间上采用隐式Crank-Nicolson方法,在空间上采用新的隐式虚拟元方法.最终,我们得到了NLSW方程的L2误差估计。

Keywords

虚拟元方法

误差分裂技术

截断函数方法

误差估计

References

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