Using function in table and plot its solution?

Questions
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1

Hello,

I have solved a differential equation using NDSolve, and then put the solution inside a Table. Now I want to call the solution from the table and plot it, or check the solution’s value for specific values of the variable t. How do I do it? I can’t manage to call the value of the solution from the Table.
I did the following:

Refine[s = NDSolve[{r\[Rho]ee'[t] == 2 \[CapitalOmega] im\[Rho]eg[t],im\[Rho]ee'[t] == 0, r\[Rho]eg'[t] == 2 \[CapitalOmega] im\[Rho]ee[t],
     im\[Rho]eg'[t] == \[CapitalOmega] (1 - 2 r\[Rho]ee[t]), r\[Rho]ee[0] == 0, im\[Rho]ee[0] == 0, r\[Rho]eg[0] == 0, im\[Rho]eg[0] == 0}, {r\[Rho]ee[t], im\[Rho]ee[t], im\[Rho]eg[t],
      r\[Rho]eg[t]}, {t, 0, 1}], (*here there is a list of conditions  for the functions*)
  r\[Rho]ee \[Element] Reals && im\[Rho]ee \[Element] Reals && r\[Rho]eg \[Element] Reals && im\[Rho]eg \[Element] Reals && \[CapitalOmega] [Element] Reals && \[Gamma]eg \[Element] Reals && 0 <= r\[Rho]ee[t]^2 + im\[Rho]ee[t]^2 <= 1];

(*Then I defined a Table and put the solution in the Table*)
\[Rho]List = Table[1, {i, 5}];
\[Rho]List[[1]] = s;

Now I want to call the first function from the solution, and plot it, and I try the following:

\[Rho]ee = \[Rho]List[[1]][[1]][[1]]
Plot[\[Rho]ee[t], {t, 0, 1}]

And I get nothing in the plot. Any help?

Thanks!

2

NDSolve, and most of the other “N” functions, demand that all variables except those that you are solving for have been previously assigned constant numeric values. And I made a few other changes.

\[CapitalOmega] = 1;
s = Refine[
        NDSolve[{
          r\[Rho]ee'[t] == 2 \[CapitalOmega] im\[Rho]eg[t],
          im\[Rho]ee'[t] == 0,
          r\[Rho]eg'[t] == 2 \[CapitalOmega] im\[Rho]ee[t],
          im\[Rho]eg'[t] == \[CapitalOmega] (1 - 2 r\[Rho]ee[t]),
          r\[Rho]ee[0] == 0, im\[Rho]ee[0] == 0, r\[Rho]eg[0] == 0, im\[Rho]eg[0] == 0},
          {r\[Rho]ee[t], im\[Rho]ee[t], im\[Rho]eg[t], r\[Rho]eg[t]}, {t, 0, 1}], 
     r\[Rho]ee \[Element] Reals && im\[Rho]ee \[Element] Reals && r\[Rho]eg \[Element] Reals && 
     im\[Rho]eg \[Element] Reals && \[CapitalOmega] \[Element] Reals && \[Gamma]eg \[Element] Reals && 
    0 <= r\[Rho] ee[t]^2 + im\[Rho] ee[t]^2 <= 1];
sols = {r\[Rho]ee[t], im\[Rho]ee[t], im\[Rho]eg[t], 
    r\[Rho]eg[t]} = {r\[Rho]ee[t], im\[Rho]ee[t], im\[Rho]eg[t], 
     r\[Rho]eg[t]} /. s[[1]];
Plot[sols, {t, 0, 1}]

10964g1.jpg
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r\[Rho]ee[t_] = sols[[1]];
Plot[r\[Rho]ee[t], {t, 0, 1}]

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3

Thanks for the answer!

But still, my problem is the following: I want to put ‘sols’ into a table in the following way:

tab = Table[1, {i, 5}]]

tab[[1]] = sols;

And then do something like

Plot[tab[[1]][[1]][t],{t,0,1}]

And it doesn’t work - do you know how to do it?

Thanks!

4

Is this close enough?

\[CapitalOmega] = 1;
s = Refine[
    NDSolve[{
      r\[Rho]ee'[t] == 2 \[CapitalOmega] im\[Rho]eg[t], 
      im\[Rho]ee'[t] == 0, 
     r\[Rho]eg'[t] == 2 \[CapitalOmega] im\[Rho]ee[t], 
     im\[Rho]eg'[t] == \[CapitalOmega] (1 - 2 r\[Rho]ee[t]), 
     r\[Rho]ee[0] == 0, im\[Rho]ee[0] == 0, r\[Rho]eg[0] == 0, im\[Rho]eg[0] == 0},
     {r\[Rho]ee[t], im\[Rho]ee[t], im\[Rho]eg[t],r\[Rho]eg[t]}, {t, 0, 1}], 
   r\[Rho]ee \[Element] Reals && im\[Rho]ee \[Element] Reals && r\[Rho]eg \[Element] Reals && 
   im\[Rho]eg \[Element] Reals && \[CapitalOmega] \[Element] Reals && \[Gamma]eg \[Element] Reals && 
    0 <= r\[Rho] ee[t]^2 + im\[Rho] ee[t]^2 <= 1];
sols = {r\[Rho]ee[t], im\[Rho]ee[t], im\[Rho]eg[t], r\[Rho]eg[t]} = {r\[Rho]ee[t], im\[Rho]ee[t],
    im\[Rho]eg[t], r\[Rho]eg[t]} /. s[[1]];
tab = Table[1, {i, 5}];
tab[[1]] = sols;
Plot[tab[[1]][[1]], {t, 0, 1}]

7501g2.jpg
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If you look at

tab[[1]][[1]]

you can see that it already has the [t] at the end of it, so adding another [t] inside your Plot is just confusing it.