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 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 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 …

Studying chemical reactions in computer simulations requires a reliable description of the
atomic interactions. While for systems of moderate size precise electronic structure …

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 …

The investigation of the impact of the vanishing of the phase-lag and its first and second
derivatives on the efficiency of a four-step Runge–Kutta type method of sixth algebraic order …

This research work is oriented in the behaviour of oscillating systems. In order to study such
problems, we deal with the solution of ordinary second order differential equations. A …

In this paper, we present two optimized eight-step symmetric implicit methods with phase-lag
order ten and infinite (phase-fitted). The methods are constructed to solve numerically the …