How to indentify the variables when plotting after solving a coupled system of ODEs?

Question

Enterprixe 2017-3-18

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/330532-how-to-indentify-the-variables-when-plotting-after-solving-a-coupled-system-of-odes

回答： Star Strider 2017-3-18

Hello, i had a system of coupled ODEs and i think i have solved it, the problem is that the variable Y which gives the output, i dont know how to tell what column is the response to the x(t), y(t), z(t) or their first derivatives. Help would be much appreciated. Here is the code

   syms x(t) y(t) z(t) p(t) Y 
p=sin((0.5+3.5*t)*t);
D1y = diff(y,t);
D2y = diff(y,t,2);
D1x = diff(x,t);
D2x = diff(x,t,2);
D1z = diff(z,t);
D2z = diff(z,t,2);
eqns=[D2x+2*x-1*y==p,D2y+(0.5*10*exp(-10*t))*D1y-x+2*y-z==0,D2z-y+2*z==0];
yode = odeToVectorField(eqns);
Yodefcn = matlabFunction(yode, 'Vars',[t Y]);
tspan = (0:0.001:10);
Y0 = [0 0,0 0,0 0];
[T,Y] = ode45(Yodefcn, tspan, Y0);
plot(T, Y)

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Answer 1

Star Strider 2017-3-18

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/330532-how-to-indentify-the-variables-when-plotting-after-solving-a-coupled-system-of-odes#answer_259289

在 MATLAB Online 中打开

The easiest way is to ask for a second output from your odeToVectorField call. It tells you the substitutions the function made to define each element in the returned column:

[yode,Sbs] = odeToVectorField(eqns);

here, the substitutions are:

Sbs =
  y
 Dy
  x
 Dx
  z
 Dz

The columns of ‘Yodefcn’ exactly reproduces those returned by odeToVectorField, and ode45 returns them in that order.

That can be used with some other assignments to automatically produce a legend that labels every line in the plot.

The Code —

syms x(t) y(t) z(t) p(t) Y
p=sin((0.5+3.5*t)*t);
D1y = diff(y,t);
D2y = diff(y,t,2);
D1x = diff(x,t);
D2x = diff(x,t,2);
D1z = diff(z,t);
D2z = diff(z,t,2);
eqns=[D2x+2*x-1*y==p,D2y+(0.5*10*exp(-10*t))*D1y-x+2*y-z==0,D2z-y+2*z==0];
[yode,Sbs] = odeToVectorField(eqns);
Yodefcn = matlabFunction(yode, 'Vars',[t Y]);
tspan = (0:0.001:10);
Y0 = [0 0,0 0,0 0];
[T,Y] = ode45(Yodefcn, tspan, Y0);
plot(T, Y)
Lgndc = sym2cell(Sbs);
Lgnds = regexp(sprintf('%s\n', Lgndc{:}), '\n', 'split');
legend(Lgnds(1:end-1), 'Location','N')