Konguetsof A, Simos T E
School of Engineering, Department of Civil Engineering, University of Thrace, Xanthi, Greece.
Comput Chem. 2002 Jan;26(2):105-11. doi: 10.1016/s0097-8485(01)00085-7.
A P-stable method of algebraic order eight for the approximate numerical integration of the Schrödinger equation is developed in this paper. Since the method is P-stable (i.e. its interval of periodicity is equal to (0, infinity)), large step sizes for the numerical integration can be used. Based on this new method and on a sixth algebraic order P-stable method developed by Simos (Phys. Scripta 55 (1997) 644-650), a new variable step method is obtained. Numerical results presented for the phase-shift problem of the radial Schrödinger equation and for the coupled differential equations arising from the Schrödinger equation show the efficiency of the developed method.
本文提出了一种用于薛定谔方程近似数值积分的八阶P稳定代数方法。由于该方法是P稳定的（即其周期区间等于(0, +∞)），因此可以使用较大的数值积分步长。基于这种新方法以及Simos提出的六阶P稳定代数方法（《物理学文献》55 (1997) 644 - 650），得到了一种新的变步长方法。针对径向薛定谔方程的相移问题以及由薛定谔方程产生的耦合微分方程给出的数值结果表明了所提出方法的有效性。
