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

Question

Chaitanya Pocha 2020-7-8

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/561422-how-to-use-for-loop-along-with-ode45-to-generate-a-series-of-plots

评论： Chaitanya Pocha 2020-7-8

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?

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Answer 1

Walter Roberson 2020-7-8

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/561422-how-to-use-for-loop-along-with-ode45-to-generate-a-series-of-plots#answer_462710

编辑：Walter Roberson 2020-7-8

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