how to use for loop along with ode45 to generate a series of plots

I'm relatively new to MATLAB. I'm trying to use ode45 to solve a second order differential and then generate a series of plots. Below is what I have done.

So, I'm given a second order differential along with boundary conditions. T(0) = 0.3 and T(1) = 1, and N that varies from 1 to 10 with an increment of 1.

This is the first function file.

function dT = func(x, T)
N = 2;
dT = [T(2); (-(4*N)-((x.^3)*T(2)))/(x.^4)];
end

This is the residual function used to solve dT/dx

function re = res(za)
[x ,T] = ode45(@func, [0.3 1], [0; za]);
re = T(end,1)-1;
end

This is the solver that I have used to generate a plot at N =2

za = fzero(@res, 50)
[x, T] = ode45(@func, [0.3 1], [0; za]);
plot(x, T(:, 1))
xlabel('Position')
ylabel('Temperature')
title('Temperature distribution in the fluid')

Okay, so the above solver gives me a plot at N =2. However, I need to get a series of 10 plots for 10 different N using a for loop. N ranges from 1 to 10 with an increment of 1. Can someone help me get 10 graphs like these?

Answer 1

[Walter Roberson]

for N = 1 : 10
    za = fzero(@(za) res(za,N), 50)
    [x, T] = ode45(@(x,T)func(x,T,N), [0.3 1], [0; za]);
    plot(x, T(:, 1), 'DisplayName', sprintf('N = %d', N));
    if N == 1
      xlabel('Position')
      ylabel('Temperature')
      title('Temperature distribution in the fluid')
      hold on
    end
    legend show
    drawnow();
end
hold off


function dT = func(x, T, N)
  dT = [T(2); (-(4*N)-((x.^3)*T(2)))/(x.^4)];
end

function re = res(za, N)
  [x ,T] = ode45(@(x,T) func(x,T,N), [0.3 1], [0; za]);
  re = T(end,1)-1;
end

[Chaitanya Pocha]

Thank you for your answer. However, I'm getting a few errors with this code, one is with the function handle, probably because of different version. I use the R2019a. I could solve this issue. However, I still get another error that says "not enough input arguments"

Can you try to modify this code to remove this error. Your help is very much appreciated.

[madhan ravi]

Did you read his answer properly?

[Chaitanya Pocha]

yeah, I read it properly, theres's an error in the function file perhaps.

[madhan ravi]

No, you didn’t. Read his second line and compare it with how you’re using it.

[Chaitanya Pocha]

True, I did that, and I got no errors finally.

However, what I'm getting is 10 graphs for only N=10. There's no graph for other N.

[madhan ravi]

Check the photo in https://www.mathworks.com/matlabcentral/answers/561422-how-to-use-for-loop-along-with-ode45-to-generate-a-series-of-plots#comment_929132 with sir Walters code and tell if they are the same.

[Walter Roberson]

The code I posted replaces all of your previous code.

I did have a typing mistake in one line so copy it again. Put it in a file such as rez10.m and save, and run the file.

The line you are having the problem on, fzero(@res, 50) does not appear in my code.

[Chaitanya Pocha]

Yeah, I finally got the plot. Thanks sir walter for this. I've accepted your answer.

Answer 2

[madhan ravi]

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html after that loop through N.