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Green's Function fo a Boundary Value Problem

  1. Nov 26, 2012 #1
    1. The problem statement, all variables and given/known data

    [tex] L[y] = \frac{d^2y}{dx^2} [/tex]

    Show that the Green's function for the boundary value problem with [itex] y(-1) = 0 [/itex] and [itex] y(1) = 0 [/itex] is given by

    [itex] G(x,y) = \frac{1}{2}(1-x)(1+y) for
    -1\leq y \leq x \leq 1\ [/itex]


    [itex] G(x,y) = \frac{1}{2}(1+x)(1-y) for
    -1\leq x \leq y \leq 1\ [/itex]


    2. Relevant equations



    3. The attempt at a solution


    Well in class we had defined [itex] L[y] = (py')' + qy [/itex] as the Strum-Liouville self-adjoint operator

    So that gives me:

    [itex] L[y] = (py')' + qy = \frac{d^2y}{dx^2} [/itex]


    Do I treat this problem like other Strum-Liouville Boundary Problems by writting it as :

    [itex] L[y] = (py')' + qy = f(x) [/itex]

    Where [itex] f(x) = \frac{d^2y}{dx^2} [/itex]

    And continue on as I usually would?

    Any help on this would be greatly appreciated!
     
  2. jcsd
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