ABSTRACT
In this paper we will develop a trigonometrically fitted Adams-Bashforth- Moulton predictor-corrector method which will be used for the approximate solution of the resonance problem of the Schrödinger equation. Our new trigonometrically fitted P-C scheme is based on the well known Adams-Bashforth-Moulton methods. In particular, they are based on the sixth order Adams-Bashforth scheme (as predictor) and on the seventh order Adams-Moulton scheme (as corrector). The application of the new algorithm to the numerical solution of the Schrödinger equation shows the efficiency of the new developed algorithm.
