後退微分法
s段BDF方法(s < 7)は次通り:
BDF1: y n + 1 − y n = h f ( t n + 1 , y n + 1 ) {\displaystyle y_{n+1}-y_{n}=hf(t_{n+1},y_{n+1})} ; (後退オイラー法)
BDF2: y n + 2 − 4 3 y n + 1 + 1 3 y n = 2 3 h f ( t n + 2 , y n + 2 ) ; {\displaystyle y_{n+2}-{\tfrac {4}{3}}y_{n+1}+{\tfrac {1}{3}}y_{n}={\tfrac {2}{3}}hf(t_{n+2},y_{n+2});}
BDF3: y n + 3 − 18 11 y n + 2 + 9 11 y n + 1 − 2 11 y n = 6 11 h f ( t n + 3 , y n + 3 ) {\displaystyle y_{n+3}-{\tfrac {18}{11}}y_{n+2}+{\tfrac {9}{11}}y_{n+1}-{\tfrac {2}{11}}y_{n}={\tfrac {6}{11}}hf(t_{n+3},y_{n+3})}