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11/25/09 04:04am

Hello All,

Using Mathematica I met a problem with solving of ODE. Maybe this problem has a non-technical, mathematical character

First step I needed to solve this system (kinetic equations for isotopic exchange)

/parameters calculated from the experimental conditions/

result := DSolve[{α'[t] == (α0 - α[t])*K1 + (αs[t] - α[t])*K2, αs'[t] == (α[t] - αs[t])*K3, α[0] == αs0, αs[0] == αs0, {α[t], αs[t]}, t]

α00[t_] = α0[t]/.result

It has an analytical solution - sum of exponents, and α0[t] behaves itself as functions like f(t)=1-p*exp(-qt), 0<p<1, q>0 on interval {0,+inf}. Also I found numerical solution using NDSolve procedure, interpolating function on the required interval {0,100} looked like the same as analytical one.

Then I needed to solve the similar system:

result := NDSolve[{α'[t] == (α00[t] - α[t])*K1 + (αs[t] - α[t])*K2, αs'[t] == (α[t] - αs[t])*K3, α[0] == αs0, αs[0] == αs0, {α[t], αs[t]}, {t,0,100}]

The difference from the first system is contained in replacing of the constant "α0" by the function "α00[t]", which is a solution of the first system.

The solution of the second system for α0[t] must look like the aforesaid exponent (I know it because I saw the solution in other software environment), but in the output there is written "The derivative is not consistent with initial conditions" or something like that, and i cannot plot α0[t] curve. I don't know what is wrong, I'm not an expert in math. I tried to put "α00[t]" as both analytical and numerical solution, but result was the same.

I saw the "Help", but didn't find any solution for my case.

Could you give me your suggestions how to solve this system? Maybe I need to change some parameters?

I work in Mathematica 5.2 for students

Thank you for your advices in advance!

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