Using loop for calculating ode with different parameter

How can I create a cycle, where I would use ode45 and be able to get a solution for 3 different values of a constant k so I don't have to change it manually.

example k=1 --> solution, then k=10 --> solution etc.

At the end, I would need to put all solutions into the same plot to compare.

Answer 1

[Eric]

Use a for loop. If k is non-linear, just put your values of interest into a vector.

 loop_i = 0;
 for k = [1 10 ....Rest of your numbers];
     loop_i = loop_i+1;
     [t{loop_i}, y{loop_i}] = ode45(...Whatever involving k);
 end

I have to admit I don't know what size outputs the function ode45() will return, so sticking them in cells was simply a safe bet for me. If you always expect the same size vector to be returned, you could use y(:,loop_i) instead, or y(:,:,loop_i), etc. If y(:,loop_i) works for you, plotting will be as easy as plot(t,y).

[Walter Roberson]

If you pass a tspan of length 2 to ode45 then it returns a variable number of results. If you pass a tspan of length 3 or more to ode45 then it returns something with that many rows, one row per time requested.

[Martin Pecha]

Thanks the loop work, however the results are in matrix as a set of 1444x4 in 1x3 matrix (I used k= 1 10 100, so thats why 3 sets). How can I assign i.e. x to 1st column in this set?

[Eric]

@Martin: You will probably want to use this instead in your loop so you don't have to deal with cells:

 %This results in y being 1444 x 4 x 3
 [t(:,:,loop_i), y(:,:,loop_i)] = ode45(...Whatever involving k);

Then assigning columns could be as simple as

 x = y(:,1,:); % Results in a 1444 x 1 x3

If you need to remove the singleton dimension, check out the squeeze() or permute() functions.

[Martin Pecha]

Thanks, this works perfectly, however new problem occured. I have defined k=1 in function. when I use loop it give 3 same results and not taking in account the k = [1 10 100] in loop. How can I change it?

[Steven Lord]

Pass k into your ODE function (the first input to the ODE solver) as an additional parameter. The description of the odefun input argument in the documentation for ode45 contains a link "Parameterizing Functions" that describes various techniques you can use to do that.