A Zero-Dissipative Runge-Kutta-Nyström Method with Minimal Phase-Lag

Table 2

Summary of the characteristics of the RKN methods.

Method	$u$	$v$	${\parallel {\tau }^{(r+1)}\parallel }_2$	${\parallel {{\tau }^{\prime }}^{(r+1)}\parallel }_2$	D.C	S.I/P.I
RKN3NEW	6	$\infty$	$2.64\times 10^{-2}$	$1.87\times 10^{-2}$	$-$	$(\mathrm{0,7.57})$
RKN3V	6	$\infty$	$2.70\times 10^{-3}$	$9.01\times 10^{-4}$	$-$	$(\mathrm{0,7.57})$
RKN4C	4	$\infty$	$4.01\times 10^{-4}$	$3.10\times 10^{-4}$	$7.37\times 10^{-5}$	$(\mathrm{0,9.33})$
RKN3HS	12	3	$1.12\times 10^{-2}$	$1.59\times 10^{-2}$	$1.83\times 10^{-2}$	$(\mathrm{0,9.42})$
RKN4G	4	5	$6.94\times 10^{-4}$	$3.13\times 10^{-3}$	$1/1440$	$(\mathrm{0,8.77})$

Note: $u$ means dispersion order, $v$ means dissipation order, D.C means dissipation constant, S.I means stability interval, P.I means periodicity interval.