Global variables to plot variables from ODE45 function

Hello,

the following code stands representative for a bigger code, in which i want to plot some variables over time that are calculated in the odefunction but are gonna be passed to the ODE solver. Is there any way to set these variables as global variables, so that I can plot them outside of the ode Function?

Like in this case to plot the variable "a", which is calculatet inside the function.

tspan= 0:.01:10;

x=1;

[t,x] = ode45(@(t,x) odefcn(x,t),tspan,x);

figure;

plot(t,a);

function [dxdt] = odefcn(x,t)

a=cos(t)*x;

dxdt = x*a;

end

Answer 1

[Torsten]

t < pi/2 is necessary:

syms t x(t)
eqn = diff(x,t) == x^2*cos(t);
conds = x(0)==1;
dsolve(eqn,conds)

ans = 

tspan= 0:.01:10;
x=1;
[t,x] = ode45(@(t,x) odefcn(x,t),tspan,x);

Warning: Failure at t=1.562403e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (3.552714e-15) at time t.

a = zeros(size(t));
for i = 1:numel(t)
    [~,a(i)] = odefcn(x(i),t(i));
end
figure;
plot(t,a); 

function [dxdt,a] = odefcn(x,t) 
a=cos(t)*x;
dxdt = x*a;
end

[Marlon]

Thank you for the answer.

I tried to implement this in the real code, however i always get the error

">> Zustandsraum_Pacjeka_App
Index exceeds the number of array elements. Index must not exceed 1.
Error in Zustandsraum_Pacjeka_App>odefcn (line 72)
rv = [x(4)-lv*x(6)*sin(x(3));       %x(3): PSI, x(4): XV', x(6): PSI'
    Error in Zustandsraum_Pacjeka_App (line 26)
    [~,a(i)] = odefcn(x(i),t(i));"

I tried to implement it like this, perhaps you could have a look at it :) :

(..)

[t,x] = ode45(@(t,x) odefcn(x,t) ,tspan,x );

a = zeros(size(t));

for i = 1:numel(t)

[~,a(i)] = odefcn(x(i),t(i));

figure;

plot(t,a);

end

function [dxdt,a] = odefcn(x,t)

(..)

vrv = [cos(x(3)+delta) sin(x(3)+delta) 0;

-sin(x(3)+delta) cos(x(3)+delta) 0;

0 0 1]*rv;

a=vrv(1);

[Torsten]

What is rv ? A column vector with three elements ?

[Marlon]

yes, exactly.

When I try to extract any variable that is dependent on state variables, I get the mentioned error message.

I noticed that It works to extract variables that are only dependent on the time and not on state variables, if I code it with "[~,a(i)] = odefcn(x,t(i));" and not "[~,a(i)] = odefcn(x(i),t(i));"

However I also need to extract variable that are calculated with state variables..

[Torsten]

If you want to extract vrv as a 3x1 vector, use

a = zeros(3,numel(t));
for i = 1:numel(t)
    [~,a(:,i)] = odefcn(x(i,:),t(i));
end

[Marlon]

Thanks for the quick answer, but when I try to plot the first row of vrv vs time

I get following error:

Error using plot

Vectors must be the same length.

Error in Zustandsraum_lin (line 62)

plot(t,vrv(:,1))

[Torsten]

Change the code according to your needs:

t = 0:1:100;
x = [t.',t.^2',t.^3']
a = zeros(3,numel(t));
for i = 1:numel(t)
    [~,a(:,i)] = odefcn(x(i,:),t(i));
end
plot(t,a(2,:))

function [dxdt,vrv] = odefcn(x,t)
  rv = [1;1;1];
  delta = 0;
  vrv = [cos(x(3)+delta) sin(x(3)+delta) 0;
        -sin(x(3)+delta) cos(x(3)+delta) 0;
        0 0 1]*rv;
end