# ODE/PDE's in Matlab

• MATLAB

## Main Question or Discussion Point

I have two PDE's. One in terms of dz and the other in terms of dt:

$$\frac{dI(t,z)}{dz}=aI(t,z) + bI^2(t,z) - cN(t,z)I(t,z)$$
and
$$\frac{dN(t,z)}{dt}=dI^2(t,z) - eN(t,z)$$

I know the function:
$$I(t)$$

I'd like advice on how to attempt this problem on matlab using the pde function. (Matlab's examples are too complex to follow).

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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?

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.

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?

Yeah sorry it can be a bit confusing when solving a pde in this way.

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

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

The first ODE modifies I(t) as it varies with z giving I(t,z).

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.

Sure, I can think of this one as being a suitable condition:

$$N(t=-\infty,z) = 0$$