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 the present paper, we will investigate a family of explicit four-step methods first introduced
by Anastassi and Simos [1] for the case of vanishing of phase-lag and its first derivative …

Our new linear symmetric semi-embedded predictor–corrector method (SEPCM) presented
here is based on the multistep symmetric method of Quinlan and Tremaine (1990), with eight …

A two stage symmetric two-step method with vanished phase-lag and its first, second, third
and fourth derivatives with low computational cost is developed in this paper for the first time …

A Runge–Kutta type (four stages) eighth algebraic order two-step method with phase-lag
and its first, second, third and fourth derivatives equal to zero is produced in this paper. We …

A family of two stage low computational cost symmetric two-step methods with vanished
phase-lag and its derivatives is developed in this paper. More specifically we produce: a two …

In this paper we introduce, for the first time in the literature, a three-stages two-step method.
The new algorithm has the following characteristics:(1) it is a two-step algorithm,(2) it is a …

A new finite difference pair is produced in this paper, for the first time in the literature. The
characteristics of the new finite diffence pair are:(1) is of symmetric two-step,(2) is four …

A low computational cost eighth algebraic order hybrid two-step method with vanished
phase-lag and its first, second, third and fourth derivatives is developed in this paper. We …

In this paper and for the first time in this scientific discipline, we introduce a new multi-stage
two-step teeming in phase algorithm with meliorated characteristics. A theoretical …