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Math Help - Green's Functions, how does one go about solving this?

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    Green's Functions, how does one go about solving this?

    f" + 2af' + (aČ + bČ)f = g(x)


    Boundary conditions: f(0) = f(1) = 0, and a and b are constants
    Last edited by kiwijoey; August 9th 2009 at 03:44 PM. Reason: Forgot Boundary Conditions
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  2. #2
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    Quote Originally Posted by kiwijoey View Post
    f" + 2af' + (aČ + bČ)f = g(x)


    Boundary conditions: f(0) = f(1) = 0, and a and b are constants
    Are you trying to find the Green's function for this problem?

    The Green's function, G(x,y), for this problem must satify these conditions:

    1) G(x,y)"+ 2aG(x,y)'+ (a^2+ b^2)G(x,y)= 0 for all x\ne y.

    2) G(0,y)= G(1,y)= 0 for all y between 0 and 1.

    3) G'(x,y)^+- G'(x,y)- = -1 where G'(x,y)^+ is the limit of G'(x,y) with respect to x as x approaches y from above and G'(x,y)^- is the limit as x approaches y from below.

    Find the solutions to (1) that satisfy G(0,y)= 0 and solutions that satisfy G(1,y)= 0. You will have two functions each with an unknown constant. Use the fact that they must match at x= y and (3) to determine those two constants.
    Last edited by HallsofIvy; August 11th 2009 at 06:38 PM.
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