How to access function's (and variable's) value in ODE45 right after each step?

[Ashkan]

first I was thinking it was very easy to obtain a variable's or function's value after each step within ode45 subfunction. But just yesterday I found out all I had done before might be incorrect! just see the MATLAB code below:

I believed the two plots should be exactly the same but they are not! I am very disappointed and confused! can someone explain why they are not the same? and if t2 and F2 are not the actual values after each step, how can I obtain actual values of variable (t) and function (F) after each step?

many thanks in advance,
Ashkan


function tdelay
clear
clc
global Fd ts i F2 t2
Fd=8;
F0=5;
ts=0.01;
i=1;

% F=(F0-Fd)*exp(-t./ts)+Fd;

[t,F]=ode45(@werely,[0 1],F0);

plot(t,F)
hold on
plot(t2,F2,'r')
end

function dF=werely(t,F)
global ts Fd i t2 F2
t2(i)=t;
F2(i)=F;
dF=(1/ts)*(-F+Fd);
i=i+1;
end

 

[mmwave]

Dear Ashkan,

Thank you for sharing your code and concerns with us. After reviewing your code, I believe I have identified the issue that is causing the discrepancy between your two plots.

In your main function, tdelay, you are calling the ode45 function to solve for the values of F at each time step. This function uses a numerical method to approximate the solution at each time step, which means that the values for t and F that are outputted by ode45 are not the exact values at each time step, but rather an approximation.

On the other hand, in your subfunction werely, you are manually calculating the values for t2 and F2 at each time step using a mathematical formula. These values are the exact values at each time step.

So, the reason why your two plots are not identical is because they are showing different values for t and F at each time step. The plot generated by ode45 is showing the approximate values, while the plot generated by your subfunction is showing the exact values.

If you would like to obtain the exact values of t and F after each step, you can do so by modifying your code to save the values outputted by ode45 at each time step, instead of just the final values. You can do this by creating two arrays, t1 and F1, and assigning the output of ode45 to these arrays at each time step. Then, you can plot these arrays instead of t and F, and you should see that they match the plot generated by your subfunction.

I hope this helps to clarify the issue for you. If you have any further questions or concerns, please don't hesitate to reach out.