Results 1 to 5 of 5

Math Help - Finding Second-Order First Derivative

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    FL
    Posts
    9
    Thanks
    1

    Finding Second-Order First Derivative

    I can't figure out how to find the second-order first derivative. Do I start with the central difference formula, or the forward/backward difference formulas?

    This is what I'm trying to derive: f'(x) = [-f(x+2h) + 4f(x+h) - 3f(x)] / 2h

    I know the finite difference formula is: f'(x) = [f(x+h) - f(x)] / h

    I thought that I might be able to use some formulas found on this page: Numerical Methods/Numerical Differentiation - Wikibooks
    Anyway, I'm stuck, and any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,619
    Thanks
    592

    Re: Finding Second-Order First Derivative

    Hey crossingdouble.

    Are you trying to find an expression for f''(x) instead of f'(x) (since you have given the difference equation for f'(x))?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    FL
    Posts
    9
    Thanks
    1

    Re: Finding Second-Order First Derivative

    No, it is for f'(x). The problem says: Prove the second-order formula for the first derivative.

    f'(x) = [-f(x+2h) + 4f(x+h) - 3f(x)] / 2h + O(h2)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,619
    Thanks
    592

    Re: Finding Second-Order First Derivative

    Is this some kind of numerical quadrature scheme?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2012
    From
    FL
    Posts
    9
    Thanks
    1

    Re: Finding Second-Order First Derivative

    Sorry for the late response. No, I don't think this is numerical quadrature. The section in my textbook said numerical differentiation. Although, I think the next section deals with adaptive quadrature. Anyway, I think this problem requires the mean value theorem and Taylor series as well. I think it's going to be more drawn out than I expected, so I'm just going to go ask my professor.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: November 4th 2011, 08:50 AM
  2. First-Order Derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 28th 2010, 07:23 PM
  3. Replies: 2
    Last Post: September 1st 2009, 10:37 AM
  4. First Order Derivative II
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: February 19th 2009, 07:48 AM
  5. A second order partial derivative
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 19th 2007, 03:52 PM

Search Tags


/mathhelpforum @mathhelpforum