We have constructed three Runge–Kutta methods based on a classical method of Fehlberg
with eight stages and sixth algebraic order. These methods have exponential order one, two …

In this paper we construct two trigonometrically fitted methods based on a classical Runge–
Kutta method of England with fifth algebraic order. The methods will be used for the …

In this paper we are constructing two explicit Runge-Kutta methods, one with tenth order of
phase-lag and constant coefficients and one with infinite order of phase-lag and variable …

A new procedure for constructing Runge–Kutta methods for an efficient integration of the
radial Schrödinger equation is developed in this paper. The new modified Runge–Kutta …

In this paper we present an optimized explicit Runge-Kutta method, which is based on a
method of Fehlberg with six stages and fifth algebraic order and has improved …

Abstract Some embedded Runge-Kutta methods for the numerical solution of the eigenvalue
Schrödinger equation are developed. More specifically, a new embedded modified Runge …

In this paper, we present an exponentially fitted four-step method for the numerical solution
of the radial Schrödinger equation. More specifically we present a method that integrates …

A new fourth-order explicit Runge–Kutta method based on an approach of Simos is
developed in this paper. Numerical experiments reveal that the new method is much more …

In this work we construct new Runge–Kutta–Nyström methods especially designed to
integrate exactly the test equation y ″=− w2y. We modify two existing methods: the Runge …

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 …