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

Table 4

Approximate range 𝑇_𝑎𝑝 and total number of iterations (N. Iter.) 𝜃₀=5𝜋/6 (𝑇_exact=11.07226s)—HdH1 and HdH2 methods.

Δ𝑡(𝑠)	HdH1	𝜀𝑟%	N. Iter.	HdH2	𝜀𝑟%	N. Iter.
1.50000	5.69404	48.6	6	8.80756	20.4	30
1,00000	7.250241	34.5	48	10.04931	9.2	26
0,10000	10.88812	1.6	75	11.01278	0.54	72
0,01000	11.05525	0.15	459	11.06660	5.1e–2	373
0,00100	11.07056	1.5e–2	2768	11.07169	5.1e–3	2768
0,00010	11.07208	1.6e–3	27681	11.07219	6.3e–4	27681
0,00001	11.07223	2.7e–4	276806	11.07224	1.8e–4	276807