Abstract
The new scheme developed in this paper is a new trigonometrically-fitted predictor-corrector (P-C) scheme based on the Adams-Bashforth-Moulton P-C methods. In particular, our predictor is based on the fifth algebraic order Adams-Bashforth scheme and our corrector on the sixth algebraic order Adams-Moulton scheme. We compared the efficiency of this new scheme against well known methods and the numerical experimentations showed that our scheme is more efficient, even when compared to methods that have been specially designed for the solution of the radial Schrödinger equation.
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