Cyclic Combination of BDF

1. Backward differentiation formulas. The BDF are as follows. Name Formula BDF1 $y_{n+1} - y_n = h f_{n+1}$ BDF2 $3 y_{n+2} - 4 y_{n+1} + y_n = 2 h f_{n+2}$ BDF3 $11 y_{n+3} - 18 y_{n+2} + 9 y_{n+1} - 2 y_n = 6 h f_{n+3}$ BDF4 $25 y_{n+4} - 48 y_{n+3} + 36 y_{n+2} - 16 y_{n+1} + 3 y_n = 12 h f_{n+4}$ BDF5 $137 y_{n+5} - 300 y_{n+4} + 300 y_{n+3} - 200 y_{n+2} + 75 y_{n+1} -12 y_n = 60 h f_{n+5}$…