Module 3: Higher order Single Step Methods
  Lecture 9: Runge-Kutta Methods
 

 

Expanding as a Taylor series about the point we obtain

Substituting for , and using (3.18), we get

(3.19)

Expanding by Taylor series and after substituting for and , we obtain

(3.20)

Substituting the expansion of in (3.12), we have

(3.21)

We now have to match (3.21) with (3.16) to find the parameters. We do this in the following manner:

We first let so that and (3.21) reduces to

(3.22)