MATLAB: How to solve a set of transcendental differential equation

for frate equation

I have to solve a couple of transcendental differential equation. Can anyone please suggest me how should I write a code for solving these equations: –
The intensity at a depth z is: –
I(z) = I₀ e^(-∫_0^1[f(z,t) A_undam + {1-f(z,t)A_dam}]dz)……………………………………(1) (The lower limit of this integration is 0 and the upper limit is 1.)
and the rate equation: – df(z,t) = -α I (z) f(z,t) dt + β N {1 – f(z, t)} dt ………………………….(2)
I have the data for α, β, Iₒ, A_undam and A_dam. I need to get f(z,t). How do I solve these two transcendental equations? Here, α, β, Iₒ are just a number like 10.34 etc, A_undam and A_dam are both column vector. Using equation (1) and (2), I need to solve for f(z,t). How should I do it?

Best Answer

Are I(z) and f(z,t) intended to be something other than scalars? You say that A_undam and A_dam are column vectors, so if f(z,t) is a scalar then f(z,t)*A_dam would be a column vector and would not be subtractable from 1 because 1 is not a column vector. To make geometric sense with A_undam and A_dam being column vectors, f(z,t) would have to be a row vector so that f(z,t)*A_dam would be a scalar. But then in the rate equation, 1 - f(z,t) would not make geometric sense.
I have to conclude that the situation cannot be as you describe it, unless "column vector" includes the degenerate case of 1 x 1 column vector.
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