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 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 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 …

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 …

The phase lag and its first, second, third, fourth, and fifth derivatives are all accounted for in a
phase-fitting method. The new system uses the fewest possible function evaluations per …

Methods for fitting the phase-lag and its first, second, third, and fourth derivatives are
incorporated into a phase-fitting strategy. The novel system is singularly P-stable and is a …

Recently, the symplectic exponentially-fitted methods for Hamiltonian systems with periodic
or oscillatory solutions have been attracting a lot of interest. As an alternative to them, in this …

The construction of high order symmetric, symplectic and exponentially fitted Runge–Kutta
(RK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions …

A phase-fitting and first derivative phase-fitting method is developed. The new scheme is
singularly P-Stable and belongs to the economic algorithms. The new method is symbolized …