Author 
Comment/Response 
Aleksei

11/25/09 04:04am
Hello All,
Using Mathematica I met a problem with solving of ODE. Maybe this problem has a nontechnical, mathematical character
First step I needed to solve this system (kinetic equations for isotopic exchange)
/parameters calculated from the experimental conditions/
K1=0.107
K2=0.541
K3=0.844
α0=0.981
αs0=0.0024
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)=1p*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!
URL: , 
