Euler's method error

  • Thread starter Moose352
  • Start date
  • #1
166
0
I understand how the (local) error for euler's method of integration is derived from the perspective of the taylor expansion and inequality. However, I don't really see why taylor's equation needs to be invoked, since the euler method can also be derived as a tangent line approximation. How then is the order of the error estimated by interpreting euler's method as a tangent line approximation?
 

Answers and Replies

  • #2
Integral
Staff Emeritus
Science Advisor
Gold Member
7,201
56
It is really the same thing. Using a Taylor series expansion, for the Euler method you truncate all but the linear terms, thus your approximation is assuming a local linear function. This is the exact same thing as using a tangent line approximation. You are assuming that the function is locally linear. When you say you are just making a tangent line approximation you are simply ignoring the fact that you are in reality just dropping the nonlinear terms of the Taylor series.
 

Related Threads on Euler's method error

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
12
Views
4K
  • Last Post
Replies
2
Views
697
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
9
Views
4K
  • Last Post
Replies
3
Views
745
  • Last Post
Replies
4
Views
3K
Top