Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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 ;-)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook