Solution of Higher-Order ODEs Using Backward Difference Method

Table 2

The implicit integration coefficients for 𝑘 from 0 to 6.

𝑘	0	1	2	3	4	5	6
𝛾^∗1,𝑘	1	−1/2	−1/12	−1/24	−19/720	−3/160	−813/60480
𝛾^∗2,𝑘	1/2	−1/3	−1/24	−7/360	−17/1440	−41/5040	−731/120960
𝛾^∗3,𝑘	1/6	−1/8	−1/80	−1/180	−11/3360	−89/40320	−5849/3628800