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 …

In this paper, we provide a simple framework to derive and analyse a class of one-step
methods that may be conceived as a generalization of the class of Gauss methods. The …

The construction of a class of nonlinear two-step methods for solving second order
oscillatory IVPs is analyzed. These methods are exact for the linear space generated by the …

The construction of exponentially fitted Runge–Kutta (EFRK) methods for the numerical
integration of Hamiltonian systems with oscillatory solutions is considered. Based on the …

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 …

In the last few decades, numerical simulation for nonlinear oscillators has received a great
deal of attention, and manyresearchers have been concerned with the design and analysis …

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 …