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 …

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 …

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 …

In this paper we develop and study new high algebraic order multiderivative explicit four-
step method with phase-lag and its first, second and third derivatives equal to zero. For the …

In this paper we will develop an explicit fourth algebraic order four-step method with phase-
lag and its first and second derivatives vanished. The comparative error and the stability …

Based on an optimized explicit four-step method, a new hybrid high algebraic order four-
step method is introduced in this paper. For this new hybrid method, we investigate the …

In this paper, we study the effects of the vanishing of the phase-lag and its first, second and
third derivatives on the effectiveness of a four-step hybrid type method of sixth algebraic …

A family of explicit linear sixth algebraic order six-step methods with vanished phase-lag and
its first derivative is obtained in this paper. The investigation of the above family of methods …

In this paper an eighth algebraic order predictor–corrector explicit four-step method is
studied. The main scope of this paper is to study the consequences of (1) the vanishing of …