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

Table 5

Approximate range 𝑇_𝑎𝑝 and total number of iterations (N. Iter.) 𝜃₀=5𝜋/6 (𝑇_exact=11.07226s)—HdH3 and HdH4 methods.

Δ𝑡(𝑠)	HdH3	𝜀𝑟%	N. Iter.	HdH4	𝜀𝑟%	N. Iter.
1.5000	8.06038	27.2	37	9.59701	13.3	23
1,00000	9.73503	12.1	32	10.39086	6.1	22
0,10000	10.98454	0.79	88	11.03597	3.3e–1	77
0,01000	11.06379	7.6e–2	547	11.06885	3.1e–2	535
0,00100	11.07140	7.7e–3	4877	11.07191	3.2e–3	3871
0,00010	11.07216	9.0e–4	27681	11.07221	4.5e–4	27681
0,00001	11.07224	1.8e–4	276806	11.07224	1.8e–4	276807