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, a new modified Runge-Kutta-Nyström method of third algebraic order is
developed. The new modified RKN method has phase-lag and amplification error of order …

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 …

A new modified Runge‐Kutta‐Nyström method of fourth algebraic order is developed. The
new modified RKN method is based on the fitting of the coefficients, due to the nullification …

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 study the connection between:(i) closed Newton-Cotes formulae of high
order,(ii) trigonometrically-fitted and exponentially-fitted differential methods,(iii) symplectic …

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 …