On a New Family of Runge–Kutta–Nyström Pairs of Orders 6(4)
Vladislav N. Kovalnogov,
Ruslan V. Fedorov,
Dmitry A. Generalov,
Ekaterina V. Tsvetova,
Theodore E. Simos,
Charalampos Tsitouras
Affiliations
Vladislav N. Kovalnogov
Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Ruslan V. Fedorov
Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Dmitry A. Generalov
Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Ekaterina V. Tsvetova
Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Theodore E. Simos
Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Charalampos Tsitouras
General Deptartment, Euripus Campus, National & Kapodistrian University of Athens, GR-34400 Psachna, Greece
In this study, Runge–Kutta–Nyström pairs of orders 6(4) using six stages per step are considered. The main contribution of the present work is that we introduce a new family of pairs (i.e., new methodology of solution for order conditions) that possesses seven free parameters instead of four, as used by similar pairs until now. Using these extra coefficients efficiently we may construct methods with better properties. Here, we exploit the free parameters in order to derive a pair with extended imaginary stability interval. This type of method may furnish better results on problems with periodic solutions. Extended numerical tests justify our effort.
