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Homework Help: Finite differences for PDE

  1. Mar 26, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that the first order derivative y'(xi) in the point xi may be approximated by

    y'(xi)= (1/12*h) * (-3yi-1 -10yi + 18yi+1 -6yi+2 + yi+3) - (1/20h) h^4*y^(5) + O(h^5)


    3. The attempt at a solution

    I think the idea is to setup a linear system and some how use taylor expansion.

    y'(xi) = a(-1)*y(xi-1) +
    a(0) *y(xi) +
    a( 1) *y(xi+1) +
    a( 2) *y(xi+2) +
    a( 3) *y(xi+3) +

    Anyone has any idea on how I can show the above?
     
  2. jcsd
  3. Mar 26, 2007 #2

    HallsofIvy

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    xi is a point in how many dimensions? 2, 3?
     
  4. Mar 26, 2007 #3
    I would assume one dimension.

    xi are discrete points.

    If anyone has any ideas on how to solve this please shout ;-)
     
    Last edited: Mar 27, 2007
  5. Mar 28, 2007 #4
    If you can give a hint for n-dimensions HallsofIvy then I am sure I can solve it for 1d ;-)
     
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