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Tips on good N-L-ODE

  1. Jun 9, 2010 #1
    I am trying to demonstrate a solver for non-linear ODE an wonder if anyone has got a tip on one which is non-trivial to solve, and has some significance to some people so that maybe someone will read my report =)

    If you got a good tip, thank you very much!
  2. jcsd
  3. Jun 9, 2010 #2
    How about this Riccati equation:

    [tex]y^{\prime} + y^2 + \alpha(x) = 0[/tex]

    (where alpha is an arbitrary function of x, and y = y(x) as well). This has no general solution (as far as I know) -- and it is very important. If you can provide an analytic solution to this, then fame and fortune is yours. ;-)
  4. Jun 10, 2010 #3
    Thank you, i will look in to that one. Although it is not an analytical solution i am working with, but a numerical. If i am not mistaking the analytical method for solving them are already known?
  5. Jun 10, 2010 #4
    Sorry, I misunderstood -- the equation I quoted has no known general solution (analytical), but I suspect there are many numerical methods already associated with it. If you apply your method, you should then do a survey on the web of other numerical techniques applied this class of equations, and then compare results.
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