求解一维Schrdinger方程的P稳定Obrechkoff两步方法

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.

A P-Stable Two-Step Obrechkoff Method for One-Dimensional Schr(o)dinger Equation

In this paper,a new kind of P-stable two-step Obrechkoff method for the ultra-high-accurate solution of a one-dimensional Schr(o)dinger equation is proposed.Improving Wang's method,a new Pstable 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(o)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.