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MATLAB ODE/PDE's in Matlab

  1. Mar 31, 2010 #1
    I have two PDE's. One in terms of dz and the other in terms of dt:

    [tex]\frac{dI(t,z)}{dz}=aI(t,z) + bI^2(t,z) - cN(t,z)I(t,z)[/tex]
    [tex]\frac{dN(t,z)}{dt}=dI^2(t,z) - eN(t,z)[/tex]

    I know the function:

    I'd like advice on how to attempt this problem on matlab using the pde function. (Matlab's examples are too complex to follow).
  2. jcsd
  3. Apr 3, 2010 #2
    I might be able to help given that I know at least a little about diff eq.s in matlab, but first:

    you say you know I(t), but in your equations I appears as a function of two variables. And if you know THAT function, then what's the use of the first equation?
  4. Apr 3, 2010 #3
    Because I know I(t) the first equation determines how I(t) varies with z thus giving I(t,z).

    I should also mention letters on the rhs "a,b,c,d,e" are constants.
  5. Apr 3, 2010 #4
    I'm still not quite getting it. When you say that you know I(t), do you mean that you know I(t,0) or something like that?
  6. Apr 3, 2010 #5
    Yeah sorry it can be a bit confusing when solving a pde in this way.

    Here's what I(t) is:
    [tex]I(t) = I_{max}exp(\frac{-t^2}{T})[/tex]

    I(t,0) = I(t).

    The first ODE modifies I(t) as it varies with z giving I(t,z).
  7. Apr 3, 2010 #6
    Aha. Okay, got it, thanks. Do you have a similar boundary condition for N(t,z)? I don't think matlab can do much with it if not.
  8. Apr 3, 2010 #7
    Sure, I can think of this one as being a suitable condition:

    [tex]N(t=-\infty,z) = 0[/tex]
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