Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Numerical DE: Theta method

  1. May 8, 2005 #1
    Hello,

    I am given the method: y_(n+1) = y_n + h f(t_n + w h, (1-w)y_n + w y_(n+1).

    I am to determine the region of absolute stability;

    I am also to determine for which w in [0, 1] is the method A(a) stable,
    i.e., the region of absolute stability contains a sector about the negative
    real axis.

    I found the root of the characteristic polynomial in the complex plane to
    be:

    z = [1 + h k (1-w) ] / [1 - h k w]

    So RAS = {hk : |z| < 1}

    Can I simply that further? I.e., can I get a more explicity formula for
    what the hk that satisfy z < 1 is?

    Also I am at a loss on how to solve for when the method is A(a) stable.
    Please help if you can. Thanks in advance.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted