非线性Schr inger方程非周期初值问题的数值方法

Numerical method of non-periodic initial problem for nonlinear Schrodinger equation

研究了非线性Schrodinger方程:iu_t-u_(xx)+βq(|u|~2)u=0,x∈R^1,0≤t≤T,非周期初值问题的数值解法.化非周期初值问题为周期问题,并构造了周期问题的Euler拟谱格式和跬跳拟谱格式,由此得到了误差估计,最后给出了具体算例和计算结果.

The numerical method of non—periodic initial problem for the following nonlinear Schrodinger equation iu_l—u_(xx)+βq(|u|~2)u=0, x∈R^1, 0≤t≤T,is considered. The non—periodic initial problem is reduced to the the periodic initial problem, Euler and leap—frog pseudospectral schemes are constructed. Morever, error estemate is obtained. Finally the numerical example and computational result are given.