Need Help Solving Two Coupled ODEs

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Alyssa Garreau 2021-4-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/816125-need-help-solving-two-coupled-odes

评论： Alyssa Garreau 2021-4-29

采纳的回答： James Tursa

在 MATLAB Online 中打开

Hi I am trying to solve two coupled ODEs simultaneously.

My equations are:

dT1/dz = -U*a1/(p1*q1*Cp1*L)*(T1 - T2) - Q*a1/(p1*Cp1)

dT2/dz = U*a2/(p2*Cp2*q2*L)*(T1 - T2)

I have tried programming Matlab in several different ways this is the code for the one I think I am the closest to solving.

function [z, T] = Term_project2
    U= 280;
    a=2*.45*3.14159;
    p1= 0.5;
    L= 8000;
    Cp1= 10;
    Q=284;
    p2= 1;
    Cp2= 15;
    q1= 0.5;
    q2= 1;
    zspan=[0:40];
    T0= [12 5];
dT(1) = -(U*a)/(L*p1*Cp1*q1)*(T1(z)-T2(z))-Q/(p1*Cp1);
dT(2) = (U*a)/(L*p2*Cp2*q2)*(T1(z)-T2(z))-Q/(p2*Cp2);
[z,T]= ode45(Term_project2(z,p1,p2,q1,q2,U,Q,Cp1,Cp2L),zspan,T0);
plot(z,T1(:,1),'-o',z,T2(:,2),'-.')
end

Errors: Unrecognized function or variable 't'.

Which doesn't make sense since I don't have t.

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Answer 1

James Tursa 2021-4-29

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https://ww2.mathworks.cn/matlabcentral/answers/816125-need-help-solving-two-coupled-odes#answer_688100

编辑：James Tursa 2021-4-29

在 MATLAB Online 中打开

The derivative function needs to have the input arguments specified. In your current code above, you have no inputs specified.

For the ode45 call, you need to pass a function handle that has only two inputs, the independent variable and the current state.

So your derivative function should look something like this:

function dTdz = Term_project2(z,T,p1,p2,q1,q2,U,Q,Cp1,Cp2L) % pass in all needed inputs
dTdz(1,1) = -(U*a)/(L*p1*Cp1*q1)*(T(1)-T(2))-Q/(p1*Cp1); % use T(1) and T(2) for T1 and T2
dTdz(2,1) = (U*a)/(L*p2*Cp2*q2)*(T(1)-T(2))-Q/(p2*Cp2);
end

And your calling code should look something like this:

U= 280;
a=2*.45*3.14159;
p1= 0.5;
L= 8000;
Cp1= 10;
Q=284;
p2= 1;
Cp2= 15;
q1= 0.5;
q2= 1;
zspan=[0:40];
T0= [12 5];
% 1st argument to ode45 below needs to be a function handle
% that takes z and T as inputs
[z,T]= ode45(@(z,T)Term_project2(z,T,p1,p2,q1,q2,U,Q,Cp1,Cp2L),zspan,T0);
plot(z,T(:,1),'-o',z,T(:,2),'-.')

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James Tursa 2021-4-29

You still have all your code mixed together. The function needs to be only the four lines I have written above. Nothing else. You could put that in a file called Term_project_soln.m

Then have your other code in a separate script file that sets the constants, calls ode45, and does the plotting.

Alyssa Garreau 2021-4-29