Mathematical Problems in Engineering / 2011 / Article / Tab 2

Research Article

Solution of Higher-Order ODEs Using Backward Difference Method

Table 2

The implicit integration coefficients for π‘˜ from 0 to 6.

π‘˜ 0123456

𝛾 βˆ— 1 , π‘˜ 1βˆ’1/2βˆ’1/12βˆ’1/24βˆ’19/720βˆ’3/160βˆ’813/60480
𝛾 βˆ— 2 , π‘˜ 1/2βˆ’1/3βˆ’1/24βˆ’7/360βˆ’17/1440βˆ’41/5040βˆ’731/120960
𝛾 βˆ— 3 , π‘˜ 1/6βˆ’1/8βˆ’1/80βˆ’1/180βˆ’11/3360βˆ’89/40320βˆ’5849/3628800

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