求解一维Schrdinger方程的P稳定Obrechkoff两步方法

A P-Stable Two-Step Obrechkoff Method for One-Dimensional Schrdinger Equation

提出一种新的高精度、高效率求解一维Schrdinger方程的Obrechkoff两步方法.通过增加奇数次高阶微商项,大幅度提高了经典Obrechkoff两步递推公式的精度.由求解Morse势束缚态本征值的数值例子表明,在精度和效率上该方法比经典方法求解一维Schrdinger方程有明显的优势.

In this paper, a new kind of P-stable two-step Obrechkoff method for the ultra-high-accurate solution of a one-dimensional Schrfdinger equation is proposed. Improving Wang＇ s method, a new P- stable two-step Obrechkoff method by adding odd derivatives of higher-order has been developed. The proposed method is effective but has high local truncation error. By using the new approach, one can obtain solutions of the well-known one-dimensional Schr^dinger equation. Numerical experiments on the well-known Morse potential demonstrate that our method has the advantage over Wang＇ s both in accuracy and efficiency.