On finite difference methods for the solution of the Schrödinger equation - ScienceDirect Skip to
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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 …

We are presenting a family of trigonometrically fitted partitioned Runge–Kutta symplectic
methods of fourth order with six stages. The solution of the one-dimensional time …

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 …

The development of optical imaging techniques has led to significant advancements in
single‐nanoparticle tracking and analysis, but these techniques are incapable of label‐free …

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 …

A family of hybrid methods with algebraic order eight is proposed, with phase-lag and its first
four derivatives eliminated. We investigate the behavior of the new algorithm and the …

We develop a family of six methods for the numerical integration of the Schrödinger equation
and related initial value problems with oscillating solution. Three of the methods are …