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Linear multistep methods - ODE's

  1. Nov 6, 2011 #1
    [PLAIN]http://img27.imageshack.us/img27/7175/52292891.jpg [Broken]

    I've managed to show it is zero stable and not consistent, and that it is not convergent because zero-stable + consistent = convergent. Now I'm stuck with the part bracketed in red. How would I choose tau and find a general solution for U^n?

    Do I just take tau=1/N and so then N=1/tau?

    For the general solution for U^n I tried doing:

    U^0 = 0

    U^1 = tau/3

    U^2 = U^1 (from the 1st equation, left hand side) = tau/3

    U^3 = U^2 = tau/3

    ...

    U^n = (n/n) tau/3. Is this correct?

    Many thanks!

    By the way, how would I go about showing the limit as required in the question?
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
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