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Laplace numerical solution

  1. Feb 9, 2009 #1
    hi there, im a bit stuck can someone help?

    i have a 5 point grid
    --_______v1
    --_______|
    --_______|
    v3-------v0-------v4
    --_______|
    --_______|
    --_______v2

    --_______ used to postion the | (y-axis) the grid is a plus sign.

    they are seprated by [tex]\delta[/tex]x and [tex]\delta[/tex]y

    i've worked out upto the second differential:
    (v3-v0/[tex]\delta[/tex]x - v0-v4/[tex]\delta[/tex]x) /[tex]\delta[/tex]x + (v1-v0/[tex]\delta[/tex]y - v0-v2/[tex]\delta[/tex]y) /[tex]\delta[/tex]y = 0

    the problem is i dont know how to get to this stage:

    v0 = 1/4 (v1+v2+v3+v4)


    thanks for your help

    pure!
     
  2. jcsd
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