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 …

Abstract An explicit optimized Runge–Kutta–Nyström method with four stages and fifth
algebraic order is developed. The produced method has variable coefficients with zero …

In this work, we give the general framework for constructing trigonometrically fitted
symplectic Runge–Kutta–Nyström (RKN) methods from symplectic trigonometrically fitted …

The standard monograph in this area is the book Exponential fitting by Ixaru and Vanden
Berghe (Kluwer, Boston-Dordrecht-London, 2004) but a fresh look on things is necessary …

The preservation of some structure properties of the flow of differential systems by numerical
exponentially fitted Runge–Kutta (EFRK) methods is considered. A complete …

This paper is devoted to the analysis of the sixth-order symplectic and symmetric explicit
extended Runge–Kutta–Nyström (ERKN) schemes for solving multi-frequency oscillatory …

The phase lag and its first derivative can all vanish when utilising a phase-fitting strategy.
Since the new method employs the highest possible algebraic order (AOR) while …

A phase-fitting, first and second derivatives phase-fitting method is produced. The new
algorithm is singularly P-Stable and belongs to the economic algorithms. The new method is …

This paper is concerned with multidimensional exponential fitting modified Runge-Kutta-
Nyström (MEFMRKN) methods for the system of oscillatory second-order differential …

An approach to phase-fitting is devised, which includes methods for fitting the phase-lag and
for fitting its first, second, and third derivatives. Singularly P-Stable, the novel system belongs …