A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation
The authors focus on the extended Runge-Kutta-Nyström (ERKN) methods proposed by \textit{X. Wu} et al. [Comput. Phys. Commun. 181, No. 11, 1873--1887 (2010; Zbl 1217.65141)]. In recent years, many ERKN methods have been presented and they are known for their numerical efficiency to solve multifrequency multidimensional ordinary differential equations. In this paper, a feasible effective technique is presented which allows one to construct ERKN methods in a very short time, even for high-order integrators. Moreover, this paper provides results which guarantee that the ERKN method obtained from the presented technique shares the same order, same symplectic property and same symmetric property with the underlying RKN method. Unfortunately, neither numerical examples nor comparisons among ERKN methods are reported.
symplectic conditions and symmetric conditions
scientific article; zbMATH DE number 6812490
scientific article