Results 1 to 2 of 2

Math Help - greens functions

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    4

    greens functions

    i am asked to find the greens function for

    U' +kU=f(x)
    with u(0)=0 and x>=0


    i found the homogenous solution and used the 4 conditions...

    my homogen soln was u=constant * exp(-kU)....

    is it possible that my G(x,s)= 0 for x<s and X>s?

    also how do i show that -u"= f(x) is not self adjoint with bc
    u(0)=0 and u'(0) +u(1)=0

    i have the greens function but the bc's dont hold for it?
    is that right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jan 2009
    From
    Australia
    Posts
    59
    My understanding is if your equation is

    Lu(x) = f(x),

    then the Green's function is the solution to

    Lg(x;s) = \delta(x-s).

    So when you solve this equation you have in the first case

    g'(x;s) +kg(x;s) = \delta(x-s)

    multiply by the integrating factor \exp(kx) you have

    \frac{d}{dx}\left[g(x;s)\exp(kx)\right] = \delta(x-s)\exp(kx),

    and integrating

    g(x;s)\exp(kx) = H(x-s)\exp(ks) + C

    Enforcing the g(0;s)=0 boundary condition and assuming x,s > 0 we can deduce C=0 and therefore

    g(x;s) = H(x-s)\exp[-k(x-s)].

    Hope this helps. You might need to give more complete details to answer the second part.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Greens theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 31st 2011, 12:29 AM
  2. greens fnc problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: May 7th 2010, 03:40 AM
  3. Greens Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 27th 2010, 02:03 AM
  4. Greens Functions for ODEs
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: November 1st 2009, 12:43 PM
  5. Greens Theorem (Need Help)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 10th 2007, 04:35 PM

Search Tags


/mathhelpforum @mathhelpforum