I'll give you some thought on part (b). Part (a) is done in a similar way.
Using Taylor expansion:
and
so
rearranging gives
Hello to everyone
I have a question with many parts that i am needing to do.
(a)Derive the 2point formula, for numerical differentiation:
What is ?
(b) Derive the same formula as (b) witht 3points formula
(c) Discretisation error in (a) and (b) is
Prove that discretisation error for f'(1), where f(x) = exp(x) is
I am knowing that
but I cannot realise how to do these parts? Can someone please showing me how to prove?
Thank you very much, I understand what you show, but I am now a small amount confused because I found
where for 3-point centered-difference formula.
Also, using Taylor expansion
where
and I now knowing
for 2-point forward difference formula but I do not understand how they got there(being very tired).
So is
or am I wrong?
You need to find out about "Big O" notation.
The big O notation gives an idea of the size of something and is used to put an upper bound on the error term in your integration formulas (and lots of other areas of math, science and computer prog.).
When we write we mean that for any value of k (even any really big finite value) then it is still possible to find a value of h sufficiently small so that .
This isn't a good explanation but a web search for "big O notation" should turn up something helpful.
I now understand what big O notation is. Thank-you for helping me know this.
But I have spent much time on trying to derive the 2point formula
using the same method as you doing for deriving but I can not find the answer.
I get
of course which is not right. What am I doing wrong?
Can someone please showing me because I can not see why, and I have used great time amounts trying to get it.