後退微分法
BDF4: y n + 4 − 48 25 y n + 3 + 36 25 y n + 2 − 16 25 y n + 1 + 3 25 y n = 12 25 h f ( t n + 4 , y n + 4 ) {\displaystyle y_{n+4}-{\tfrac {48}{25}}y_{n+3}+{\tfrac {36}{25}}y_{n+2}-{\tfrac {16}{25}}y_{n+1}+{\tfrac {3}{25}}y_{n}={\tfrac {12}{25}}hf(t_{n+4},y_{n+4})}
BDF5: y n + 5 − 300 137 y n + 4 + 300 137 y n + 3 − 200 137 y n + 2 + 75 137 y n + 1 − 12 137 y n = 60 137 h f ( t n + 5 , y n + 5 ) {\displaystyle y_{n+5}-{\tfrac {300}{137}}y_{n+4}+{\tfrac {300}{137}}y_{n+3}-{\tfrac {200}{137}}y_{n+2}+{\tfrac {75}{137}}y_{n+1}-{\tfrac {12}{137}}y_{n}={\tfrac {60}{137}}hf(t_{n+5},y_{n+5})}