Module 7: Multistep Methods
  Lecture 23: Multistep Methods for Special Equations of the Second Order
 

 

Using integration by parts, we get

(7.40)

From

where denotes the partial sum of the harmonic series.

Thus it follows

(7.41)

Multiplying both sides of (7.41) by (7.40), we thus find

There follows the recurrence relation

The numerical values of for a few values of m are given in the following table:

m

0

1

2

3

4

5

6

1

0

Formula (7.38) is used in much the same manner as the Adams-Bashforth formula. Once the values are known, can be calculated explicitly, without iteration.

For and stormer's formula reduces to the simple rule

(7.42)