Solving Time Dependent ODEs in MATLAB: Troubleshooting and Parameter Adjustment

[physchemmath]

Have been struggling with errors galore on this one. I am not too conversant with ODEs in MATLAB. The problem is as follows. I have to solve these two ODEs for A1 and A2.

A1dot = k2*A2 - k1*A1 - k3*A1/(k4 + A1) + R
A2dot = k1*A1 - k2*A2

Here R is a function of time defined as follows:

R = 5, when 7<t<7.2
R=0 otherwise

R is periodic and this pattern repeats. Like R takes the value 5 when 7<t<7.2, when 14<t<14.2, 21<t<21.2 and so on, and is zero everywhere else.

My code for obtaining the vector of differentials is as follows. It takes in t, A, T and R. The T is a time vector for the R parameter. I use the interp1 command as outlines in a sample MATLAB time dependent ODE code.

function dA = trial(t,A,T,R)
Rin = interp1(T,I,t);

V1 = 40; V2 = 100; k1 = 0.2; k2 = 0.2;k3 = 2; k4 = 0.003;

dA(1) = k2*A(2) - k1*A(1) - (k3*A(1))/(k4 + A(1)) + Rin;
dA(2) = k1*A(1) - k2*A(2);
dA = dA(:);

end

I then call this at the command line. I define R suitably using a for loop (using rem and other stuff) and define T to be the same as t0:1:tf as in the ODE tspan.

Then I solve for A.

[t,A]=ode15s(@trial, [to,tf],Anot,[],T,R);

I seem to be getting strange plots. I am concerned if the above method as such works, or the problem is with my parameter values (of which am not too sure as yet). So if the above code and the way of doing it is right, I can go about changing parameters and seeing.

Any help is highly appreciated.

Thanks..

 

[mmwave]

Thank you for sharing your code and the problem you are facing. Solving ODEs in MATLAB can be tricky, especially when there are time-dependent variables involved. From your code, it seems like you have a good understanding of how to set up the ODEs and use the interp1 function to define the time-dependent variable R. However, there are a few things that I noticed that may be causing the strange plots you are getting.

Firstly, in your code, you are using the ode15s solver, which is designed for stiff ODEs. Stiff ODEs are those that have very different time scales for different variables. In your case, the variables A1 and A2 have different rates of change, so using ode15s may not be the best choice. I would recommend trying the ode45 solver, which is better suited for non-stiff ODEs.

Secondly, in your code, you are defining R as a function of time, but in the ODEs, you are using the variable Rin, which is a function of the time vector T. This may be causing some confusion and may be why you are getting strange plots. I would suggest using the same variable for R in your ODEs, and also make sure that it is a function of time and not the T vector.

Lastly, it is always a good idea to check your parameter values and make sure they are reasonable for the system you are modeling. It is possible that some of the strange plots you are getting may be due to unrealistic parameter values.

I hope this helps you in solving your problem. If you continue to face issues, I would suggest seeking help from a colleague or a MATLAB expert who can help you debug your code and find the source of the issue. Good luck!