Go Back   Physics Help Forum > College/University Physics Help > Advanced Mechanics

Advanced Mechanics Advanced Mechanics Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Feb 27th 2013, 04:21 PM   #1
Member
 
Join Date: Feb 2013
Location: Greater St. Louis area
Posts: 43
Taylor derivation of three-point forward difference formula

I have a test early next week on using the Taylor series.

Does the attached derivation look correct and is the error term correct?

Thank you all for your help so far, especially Dr. Phil.

Last edited by roger; Mar 31st 2015 at 01:55 PM.
roger is offline   Reply With Quote
Old Feb 28th 2013, 10:57 AM   #2
Member
 
Join Date: Feb 2013
Location: NM
Posts: 94
Originally Posted by roger View Post
I have a test early next week on using the Taylor series.

Does the attached derivation look correct and is the error term correct?

Thank you all for your help so far.
What you have done (correctly) is to verify the given equation - it might be fun to try to derive it from scratch. I made a table with 1st and 2nd differences, including backward extrapolation to (t-tau)
Code:

t-tau |Extrapolate   |                  |                          |
      |              |Extrapolate       |                          |
t     |f(t)          |                  |f(t+2tau)-2f(t+tau)+f(tau)|
      |              |f(t+tau)-f(t)     |                          |Error Term
t+tau |f(t)+..+..+.. |                  |f(t+2tau)-2f(t+tau)+f(tau)|
      |              |f(t+2tau)-f(t-tau)|                          |
t+2tau|f(t)+2..+4..+8|                  |                          |
Since we are neglecting the 3rd difference, it is the Error Term. Thus the 2nd difference is assumed to be constant, allowing you to calculate the 1st difference between t and t-tau. Then set

f'(t) = [sum of 1st differences]/(2 tau) = [f(t+tau) - f(t-tau)]/(2 tau)

That should produce the desired formula.

Looking at the "explicit expression" for the error term -- when you take 4(A) - (B), isn't it -(2/3)tau^3 f'''(t) ? So the final expression would be (1/3)tau^2)|f'''(t)| ?

If you try to complete the derivation as outlined above, you can also extrapolate the error term back to see how it affects f'(t).

[BTW - for math help you can also try the forums at www.FreeMathHelp.com - they have a working LaTeX over there that makes it easier to "type" math.]
__________________
DrPhil (not the TV guy)
If we knew what we were doing, we wouldn't have to do it.

Last edited by DrPhil; Feb 28th 2013 at 11:19 AM. Reason: sign error in 2nd diff.
DrPhil is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > Advanced Mechanics

Tags
derivation, difference, formula, forward, taylor, threepoint



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Path difference of two series of monochromatic waves raech a point on screen ling233 Light and Optics 1 Dec 7th 2014 11:18 AM
Taylor expansion, centered difference formula, third derivative roger Advanced Mechanics 2 Feb 28th 2013 05:14 PM
Please explain the Taylor expansion in Radiation yungman Advanced Electricity and Magnetism 1 Jun 27th 2011 05:40 PM
Help with derivation of potential involve moving point charge. yungman Advanced Electricity and Magnetism 10 May 4th 2011 01:35 AM
Forward and Backword representation of a plane wave in a medium abaset Light and Optics 0 Feb 15th 2009 12:42 PM


Facebook Twitter Google+ RSS Feed