In this paper we present the recent development in the numerical integration of the
Schrödinger equation and related systems of ordinary differential equations with oscillatory …

In this work we review single step methods of the Runge–Kutta type with special properties.
Among them are methods specially tuned to integrate problems that exhibit a pronounced …

In this article, we develop an explicit symmetric linear phase-fitted four-step method with a
free coefficient as parameter. The parameter is used for the optimization of the method in …

In this paper, we investigate the connection between The study of multistep symplectic
integrators is very poor although in the last decades several one step symplectic integrators …

In the present paper we compare the two methodologies for the development of
exponentially and trigonometrically fitted methods. One is based on the exact integration of …

In this article we develop a family of three explicit symmetric linear four-step methods. The
new methods, with nullified phase-lag, are optimized for the efficient solution of the …

The standard monograph in this area is the book Exponential fitting by Ixaru and Vanden
Berghe (Kluwer, Boston-Dordrecht-London, 2004) but a fresh look on things is necessary …

In the present paper we develop a new methodology for the development of efficient
numerical methods for the approximate solution of the one-dimensional Schrödinger …

With this paper, a new algorithm is developed for the numerical solution of the one-
dimensional Schrödinger equation. The new method uses the minimum order of the phase …

In this paper we present a new method for the numerical solution of the time-independent
Schrödinger equation for one spatial dimension and related problems. A technique, based …