解Schrodinger方程u_(t)=iu_(xx)的线方法

THE METHOD OF LINES FOR SOLVING SCHRDINGER EQUATION u_(t)=iu_(xx)

对具有周期解的Schrodingcr方程u_=iu_(xx)(i^2=-1),用线方法构造了任意阶精度O(Δt^p+△x^(2q))(p,q为自然数)的两层和三层显格式。讨论了两层格式1≤p≤4,1≤q≤5及三层格式p=2,4,6,8,10,1≤q≤5的情形,得到了一系列格式,其精度和稳定性都优于现有格式。

Two-level and three-level exelicit difference schemes with arbitrary order accuracy O (△t^p+△x^(2q))(p,q-positive integer)for schrodinger equation u_l=iu_(xx)(i^2= -1) having periodic solution is established by the method of lines. The case of 1 ≤p≤4, 1 ≤q≤5 for two-level schemes and p=2, 4, 6, 8, 10; 1≤q≤5 for three-level schemes are discussed .A number of schemes is obtained, their accuracy and stability are all much better than those of the known schemes.