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Numerical Differentiation: Difference approximation on numerical data

  1. Oct 27, 2008 #1
    1. The problem statement, all variables and given/known data
    I am given a table of data derived from experiment. A force (F) is applied to a spring and the extension (x) is measured and recorded. An additional column of data for the derivative (dF/dx) is also provided.

    Here is the data:
    x(m) F(kN) df/dx (kN/m)
    0.0 0.0 5.0
    0.03 0.3 10.2
    0.06 0.5 4.3
    0.12 0.7 5.2
    0.2 1.8 8.2
    0.22 1.9 1.1

    The task is: using a difference approximation ( I think this is either backward, forward or central difference approximation), estimate the numerical value of the derivative dF/dx at x=0.16 based on the values provided in the table.

    2. Relevant equations
    None given

    3. The attempt at a solution
    None so far. Since I don't know how to go about it.

    I know the solution to this must be very simple, but it just won't filter into my brain.
  2. jcsd
  3. Oct 27, 2008 #2


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    Staff Emeritus
    Science Advisor

    If you "this is either backward, forward or central difference approximation" you surely must know what those things are! Try them.
  4. Oct 27, 2008 #3
    OK, something has filtered: since x=0.16 is not part of the given data ( and I don't have its corresponding y value), I cannot include x=0.16 as part of the backward,forward or central difference methods.

    If I work with the numbers around the 0.16 value, ie. 0.12 and 0.22:
    Backward difference: slope = (0.7-0.5)/(0.12-0.06) = 3.33

    Forward difference: slope = (1.9-1.8)/(0.22-0.20) = 5

    Central Difference therefore: slope = (3.33+5)/2 = 4.17

    But this approach cannot be correct, because the value of dF/dx between x=0.12 and x=0.2 is in the range of 5.2 and 8.2. So I would expect dF/dx for x=0.16 to be between 5.2 and 8.2. However, 4.17 obtained is not within that range.

    Apparently the data is not necessarily accurate, so maybe this is correct? It will be correct if my approach is correct. And that is the question right now. Can I what I did?
    Last edited: Oct 27, 2008
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