非线性Schrdinger方程的一个新的高精度守恒差分格式

A New High Accurate and Conservative Finite Difference Scheme for Nonlinear Schrdinger Equations

对一类非线性Schrdinger方程提出了1种新的高精度守恒差分格式,证明了该格式保证离散电荷和离散能守恒,而且证明了收敛性和稳定性。通过数值试验获得如下结论,该格式在提高计算速度的同时,极大地提高了计算精度。

In this paper,we present a new high accurate and conservative finite difference scheme for nonlinear Schrdinger type equations.It is proved that the scheme preserves two conservative quantities and is convergent and stable.The numerical results show that the scheme has higher precision than the other implicit schemes.