This paper presents a summary of various localized collocation schemes and their
engineering applications. The basic concepts of localized collocation methods (LCMs) are …

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 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 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 …

We use a methodology of optimization of the efficiency of a hybrid two‐step method for the
numerical solution of the radial Schrödinger equation and related problems with periodic or …

The development of a new five-stages symmetric two-step method of fourteenth algebraic
order with vanished phase-lag and its first, second, third and fourth derivatives is analyzed in …

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 …

In this paper, we will develop a four-stage high algebraic order symmetric two-step method
with vanished phase-lag and its first up to the fourth derivative. For the proposed method, we …

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 …