Summing results of ode45

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gorilla3 2017-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/361211-summing-results-of-ode45

评论： Jan 2017-10-18

Hello, using ode45 I solved 3 differential equations. I now want to create a function x that adds all the 3 components of the diff equations. Could you help me set it up?

Fx=@(t,xqxc)[ (-xqxc(1)+G_q .*(q-q_b)./q_b)./tau_q ;               
                                (-xqxc(2) +0.3+3.*tanh(Pa_co2./Pa_co2_b -1.1))./tau_co2 ]
[t, xqxc]=ode45(F,[0 100], [0 0 0]);
xq= xqxc(:,1);
xc= xqxc(:,2);
syms xm(t)
[V] = odeToVectorField(diff(xm, 2) == (-tau2*diff(xm) -xm)/tau1^2)
M = matlabFunction(V,'vars', {'t','Y'})
sol = ode45(M,[0 20],[2 0]);
x= sol+ xc -xq;

the error I get is Undefined operator '+' for input arguments of type 'struct'.

Error in CBF_v2 (line 56) x= sol+ xc -xq;

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Torsten 2017-10-17

Solve all equations simultaneously (7 as far as I can see).

This will resolve all your problems.

Best wishes

Torsten.

gorilla3 2017-10-17

Oh, I made such a silly mistake! Thank you, Torsten!!

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回答（1 个）

Jan 2017-10-15

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sol = ode45(...) replies a struct, as the error message tells clearly. Either use:

x = sol.y + xc - xq;

Or use two outputs

[t2, x2] = ode45(...)

You obtain xc from t=0 to 100, but the 2nd integration goes from 0 to 20. Are you sure that you can add them directly? Is this meaningful?

You provide an initial with 3 elements in:

[t, xqxc] = ode45(F,[0 100], [0 0 0]);

But F replies a [2 x 1] vector only.

I asked this in multiple ways but I really don't know how to solve the problem. I need a system of two 1st order diff eq and one 2nd order diff eq. I tried numerous approaches, please help me. This is how far I got:

Fx=@(t,xqxc)[ (-xqxc(1)+G_q .*(q-q_b)./q_b)./tau_q ;               
                                (-xqxc(2) +0.3+3.*tanh(Pa_co2./Pa_co2_b -1.1))./tau_co2;
      %2nd order diff:    xm'' = (-tau2* xm' -xm)/tau1^2 
                         %xm' ??
                          %xm'' 
                              (-tau2.*xqxcxmxm1(4) - xqxcxmxm1(3))./tau1.^2]
[t, xqxc]=ode45(F,[0 100], [0 0 0]);
xq= xqxc(:,1);
xc= xqxc(:,2);
xm= xqxc(:,3);
xm1= xqxc(:,4);
x=xm+ xc -xq;

Jan 2017-10-18

You can convert the 2nd order system to a 1st order system easily. Then you can integrate both trajectories together. Or you define tspan as a vector, such the output of the integrator is calculated for the same time points. Then you can add the trajectories directly.

But currently you integrate one trajectory from 0 to 100, and the other from 0 to 20. Then it does not look logical to sum the trajectories.

Summary: I still do not understand exactly, what you are asking for.

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