Method for the Woods-Saxon Potential and P?schl-Teller Potential

In this paper, we focus on the new kind of P-stable two-step Obrechkoff method for the ultra-high-accurate solution of a one-dimensional Schrdinger equation.Through improving the Wang's method, we develop a new kind of P-stable two-step Obrechkoff method by adding the odd higher-order derivatives. This proposed method is very effective but has very high local truncation error. We apply our new method to the one-dimensional Schrdinger equation such as the well-know Woods-Saxon potential and Pschl-Teller potential. Their numerical solution testified that the new method is very reliability.