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

 

The numerical values can now be easily found from these recurrence relations and are given as under:

m

0

1

2

3

4

5

6

1

We also note the relation

or

comparing the coefficients of , we obtain

(7.11)

Formula (7.9) is used like the Adam- Bashforth formula except that now only the values are known and (7.9) is used to determine . Since occurs as an argument in in the right hand term of (7.9), this equation now represents a nontrivial equation for . In general, it will not be possible to solve this equation explicitly. Fortunately, the special from of the equation suggests an iteration procedure which furnishes the solution very rapidly if is sufficiently small.