5次非线性Schrdinger方程的一个线性化4层紧致差分格式

The Linearized Four-Level Compact Finite Difference Scheme for the Quintic Nonlinear Schrdinger Equation

对5次非线性Schrdinger方程提出了一个线性化4层紧致有限差分格式,引入"抬升"技巧,运用标准的能量方法和数学归纳法建立了误差的最优估计,证明数值解在空间和时间2个方向分别具有4阶和2阶精度.数值实验对理论结果进行了验证,并通过对比表明该文格式在保持精度相当的前提下较已有格式具有更高的计算效率.

In this paper,a linearized four-level compact finite difference scheme for the nonlinear Schrodinger equation involving quintic term is proposed.By introducing a "lifting" technique,the optimal error estimate is established by using standard energy method and mathematical induction.It is proved that the numerical solution has fourth-order and second-order accuracy in space and in time,respectively.Numerical experiments are given to verify the theoretical results and compared with the existing results.The results show that the proposed scheme has higher computational efficiency under the condition of maintaining the accuracy.