Module 7: Multistep Methods
  Lecture 19: Multistep Methods (Contd.)
 

 

Adams-Bashforth Method in terms of Ordinates :

Now if we assume that , w here is a constant and is an integer, and write . Then, the first backward difference of the function at the point is defined by

Higher backward differences are defined by

, so that for instance

If we also put . One can easily verify by induction that

(7.7)

where denotes the binomial coefficient