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

Table 1

Coefficients of H_m,n type operators versus internal forces error order.

Order	1	2	3	4	5	6	7	8
𝑎0	1	−6	24	60	360	840	6720	15120
𝑏0	−1	6	−24	−60	−360	−840	−6720	−15120
𝑎1	—	−2	6	24	120	360	2520	6720
𝑏1	1	−4	18	36	240	480	4200	8400
𝑎2	—	—	—	3	12	60	360	1260
𝑏2	−1/2	1	−6	−9	−72	−120	−1200	−2100
𝑎3	—	—	—	—	—	4	20	120
𝑏3	—	—	1	1	12	16	200	300
𝑎4	—	—	—	—	—	—	—	5
𝑏4	—	—	—	—	−1	−1	−20	−25
𝑎5	—	—	—	—	—	—	—	—
𝑏5	—	—	—	—	—	—	1	1