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Solution for a nonlinear PDE

  1. Jun 26, 2011 #1
    For a general dynamic system: dXi/dt = Fi(X1, X2,...,Xn), i=1,...,n,
    Q.1
    do you have some ideas of the existence conditions of following PDE:
    a) (grad U, grad U + F) = 0 in n-dimension domain, (,) is inner product;
    b) U >=0

    Does it need a first type or second type of boundary condition?

    Q.2
    If solution does exist, how to solve it numerically?
    - I tried to write in differential equation in matrix format, then apply Newton method. It is very difficult to have a converge scheme.

    A more detailed simple example is attached to explain the solution that I tried.

    Many thanks for your ideas or comments
     

    Attached Files:

    Last edited: Jun 26, 2011
  2. jcsd
  3. Jun 29, 2011 #2
    I despair of finding a general convergence scheme as convergence is very sensitive to the nature of Fi's.
     
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