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Finite Differences

  1. Aug 23, 2008 #1
    Given the elevations of five points that are equally spaced by distance 'h' in a horizontal direction, derive a general expression to determine the second derivative of slope at the central point with an accuracy of order h3

    If elevation is given by 'z' and horizontal distance by 'x', use your result to calculate d2z / dx2 at x=10

    x | 0 | 5 | 10 | 15 | 20
    z | 6 | 7 | 9 | 10 | 9


    I am stumped at this question with no idea where to start mainly cos its asking for the second instead of the first derivative which would just mean fi = (-fi-1 + fi+1) / (-xi-1 + xi+1)

    Also the fact that its accuracy of order h3 rather than h2 or h4 etc...

    Help? I'm thinking a matrix will be involved in this...
     
  2. jcsd
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