本文对带波动算子的非线性~Schr"odinger~方程提出了一个线性的紧致差分格式,从而解决了该方程的周期初值问题. 通过先验估计和能量法,证明了格式的无条件稳定性和无穷模误差,且证得格式的收敛阶为~O(h[4]+tau[2]),最后通过一组数值实验验证了理论结果。
李鑫
,
张鲁明
,
柴光颖
. 带波动算子的非线性Schrodinger方程的线性紧格式 (英)[J]. 华东师范大学学报(自然科学版), 2016
, 2016(3)
: 1
-8
.
DOI: 2016.03.001
In this paper, a linear compact finite difference scheme is proposed for the nonlinear Schr"odinger equation with wave operator (NLSEWO). Thus, the periodic initial value problem of the NLSEWO is solved. The unconditional stability and convergence in maximum norm with order O(h[4]+tau[2]) are proved by the prior estimations and the energy method. Those theoretical results are demonstrated by a numerical experiment.
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