Georgios Psihoyios

TL;DR: In this paper, a trigonometrically fitted predictor-corrector (P-C) scheme was developed, which is based on the well-known two-step second-order Adams-Bashforth method (as predictor) and on the third order Adams-Moulton method as corrector.

TL;DR: In this paper, a trigonometrically fitted predictor-corrector (P-C) Adams-Bashforth-Moulton method is constructed, which is based on the third-order Adams-bashforth scheme as predictor and the fourth-order Moulton scheme as corrector.

Abstract: In this paper an exponentially-fitted multiderivative method is developed for the numerical integration of the Schrodinger equation. We call the method multi-derivative since it uses derivatives of orders two and four. An application to the resonance problem of the radial Schrodinger equation indicates that the new method is more efficient than the Numerov method and other known methods found in the literature. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

TL;DR: In this article, an explicit hybrid symmetric four-step method of algebraic order six is developed for periodic orbital problems, and numerical comparative results demonstrate the efficiency of the method presented here.

TL;DR: In this article, an exponentially fitted and trigonometrically fitted predictor-corrector class of methods is developed for the numerical solution of initial value problems with oscillating solutions, which represent a totally new area of application for the explicit advanced step-point or EAS methods developed by Psihoyios and Cash Numerical examples.