Module 2: Single Step Methods
  Lecture 5: Convergence of Euler's Method
 

 

To proceed further, we need the following lemma.

Lemma: If satisfies (2.5) and then

(2.6)

Proof of the Lemma: The first inequality of (2.6) follows by induction. It is trivially true for . Assuming that is true for we have from (2.5)

Hence (2.6) is true for , and thus for all