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PDE U_t = aU_xy (mixed derivatives)

  1. Feb 10, 2010 #1
    I am trying to solve

    (1) U_t = 2bU_xy (as part of U_t = aU_xx + 2bU_xy + cU_yy)

    using centred finite difference method. When a > 0 everyhing is OK but when a < 0 I get some oscillation problems.

    My questions are:

    1. is there a pde theory for (1)?
    2. what is the 'motivation' for (1) in terms of information flow to and from boundaries/
    3. maybe my fdm schemes destroy ellipticity which is the reason why I get oscillations.
    4. These oscillations seem to be related to the initial condition in some way but I have not figured it out

    thanks for any help!
  2. jcsd
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