About the Use of the HdHr Algorithm Group in Integrating the Movement Equation with Nonlinear Terms

Table 3

Approximate range 𝑇_𝑎𝑝 and total number of iterations (N. Iter.) 𝜃₀=𝜋/6 (𝑇_exact=6.392568s)—HdH3 and HdH4 methods.

Δ𝑡(𝑠)	HdH3	𝜀𝑟%	N. Iter.	HdH4	𝜀𝑟%	N. Iter.
1,00000	6,317839	1.2	7	6.345348	0.74	6
0,10000	6.390137	3.8e–2	31	6.391563	1.6e–2	31
0,01000	6.392336	3.6e–3	302	6.392475	1.5e–3	260
0,00100	6.392545	3.6e–4	1599	6.392559	1.4e–4	1599
0,00010	6.392566	3.1e–5	15982	6.392567	1.5e–5	15982
0,00001	6.392568	1.e–5	159815	6.392568	1.e–5	159815