带波动算子的非线性Schrdinger方程的线性紧格式（英文）

A linear compact scheme for the nonlinear Schrdinger equation with wave operator

本文对带波动算子的非线性Schrdinger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+τ~2),最后通过一组数值实验验证了理论结果.

In this paper,a linear compact finite difference scheme is proposed for the nonlinear Schrodinger 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 ＋ τ^2） are proved by the prior estimations and the energy method.Those theoretical results are demonstrated by a numerical experiment.