Abstract:

In this paper, a new kind of P-stable two-step Obrechkoff method for the ultrahighaccurate solution of a onedimensional Schrödinger 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 Schrödinger equation. Numerical experiments on the well-known Morse potential demonstrate that our method has the advantage over Wang’s both in accuracy and efficiency.

Key words: Obrechkoff method; one-dimensional Schrdinger equation; P-stable