摘要
在量子力学、等离子物理等许多学科中,均有大量的Schrdinger型方程,其数值求解具有重要的物理意义。本文提出了数值求解二维线性常系数Schrdinger方程的两个ADI格式(P—R格式和M—F格式),通过Von-Neumann方法判断出这两个格式均是无条件稳定的。运用Taylor展开,得出这两个格式在点处的截断误差分别为O(k2+h2)和O(k2+h4)。数值实验中,固定h,变动k,画出每次的误差曲线,验证了该格式的无条件稳定性;数值实验还表明,用这两个交替方向隐格式计算比用通常的C-N格式所消耗的CPU时间大大减少,因而该格式具有一定的实际意义。
In this paper P-R and M-F ADI scheme for two-dimension linear constant coefficient Schrodinger type equations are prevailed. There are two steps calculating problems with these schemes. We just need solute linear equations with triple diagonal coefficient matrix in each step. Using Von-Neumann method, we know these schemes are unconditionally stable .With Taylor expansion, we get their truncation errors at the point ul,m^n＋1/2 being O（k^2＋h^2） and O（k^2＋h^4）, separately. During the numerical experiment, fixing h and modifying k , we can plot every time error curve. The results show that P-R and M-F alternation direction implicit scheme are unconditionally stable. Numerical experiment also shows that these schemes cost less CPI.J time than C-N scheme.
出处
《安庆师范学院学报（自然科学版）》
2007年第4期4-6,共3页
Journal of Anqing Teachers College(Natural Science Edition)
