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ODE with Neumann Bound

  1. Oct 4, 2010 #1
    I am new to differential equations, any help would be great.

    I have a ODE of the second order u''x = e^x over the domain [1, 1] where u'(0) = 0 is a Neumann boundary on the ODE. I am trying to approximate the solution using the finite differences method, I can do Dirichlet boundaries with finite differences with no problem however the Neumann boundaries are a problem.

    The second-order finite difference is
    (e^(x - h) - 2*e^(x) + e^(x + h)) / h^2

    where h is the computed interval (change in x) across the domain.

    How can you model the approximation so that the first derivative at u'(0) = 0 is taken into account. The values I am getting are nothing like the exact solution that I have computed. I am looking to learn this procedure so can anyone point me to the algorithm for this?

    Thank you.
  2. jcsd
  3. Oct 4, 2010 #2
    Maybe my question was not properly worded.

    I just want to know how to apply a Neumann boundary on the first derivative (e.g., U'(x) = alpha) with a second-order ODE using finite differences - e.g. U''(x) = f(x)

    Is this even possible?

    Thanks again
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