Solution of Higher-Order ODEs Using Backward Difference Method

Table 1

The explicit integration coefficients for 𝑘 from 0 to 6.

𝑘	0	1	2	3	4	5	6
𝛾1,𝑘	1	1/2	5/12	3/8	251/720	95/288	19087/60480
𝛾2,𝑘	1/2	1/6	1/8	19/180	3/32	863/10080	275/3456
𝛾3,𝑘	1/6	1/24	7/240	17/720	41/2016	731/40320	8563/518400