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Solve second order ode with Green's functions

  1. Jun 23, 2013 #1
    -u''(z)+α2u(z)=f(z), u(0)=g(z), u(z)=0 as z→∞

    -u''(z)+α2u'(z)=f(z), u(0)=g(z), u(z)=0 as z→∞

    I am interested to solve these two boundary problems using Green's functions. It is noticed that z is complex variable. Can someone help me to do this?
  2. jcsd
  3. Jun 26, 2013 #2
    Well, first things first, find your green's function for the operator given.

    In other words, solve -G''(z;z') + [a^2]G(z;z') = diracdelta(z - z')

    Then simply integrate the product of G(z;z') with f(z') w.r.t z' and you're done :)
    Last edited: Jun 27, 2013
  4. Jun 27, 2013 #3


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    g(z) is the initial condition; integrating G(z;z') against f(z') should give the solution in this case, although...

    Is z the only variable in this DE? How can the initial condition u(0) = g(z) depend on z?
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