Our new trigonometrically fitted predictor–corrector (P–C) schemes presented here are based on the well known Adams–Bashforth–Moulton methods: the predictor is based on the fifth order Adams–Bashforth scheme and the corrector on the sixth order Adams–Moulton scheme. We tested the efficiency of our newly developed schemes against well known methods, with excellent results. The numerical experiments showed that at least one of our schemes is noticeably more efficient compared to other methods, some of which are specially designed for this type of problem. It is also worth mentioning that this is the first time that sixth algebraic order trigonometrically fitted Adams–Bashforth–Moulton P–C schemes are used to efficiently solve the radial Schrödinger equation.
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Psihoyios, G., Simos, T. Sixth algebraic order trigonometrically fitted predictor–corrector methods for the numerical solution of the radial Schrödinger equation. J Math Chem 37, 295–316 (2005). https://doi.org/10.1007/s10910-004-1471-7
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DOI: https://doi.org/10.1007/s10910-004-1471-7