Extract a value from a list of InterpolatingFunction

Question

By running the code

n = 5;
U[t_] := Table[Subscript[u, i][t], {i, 0, n}];
lines = NDSolve[{eqns, initc}, U[t], {t, 0, T}]

I get the output

{{u_0[t]->InterpolatingFunction[{{0.`,5.`}},"<>"][t], 
  u_1[t]->InterpolatingFunction[{{0.`,5.`}},"<>"][t],
  u_2[t]->InterpolatingFunction[{{0.`,5.`}},"<>"][t], 
  u_3[t]->InterpolatingFunction[{{0.`,5.`}},"<>"][t], 
  u_4[t]->InterpolatingFunction[{{0.`,5.`}},"<>"][t], 
  u_5[t]->InterpolatingFunction[{{0.`,5.`}},"<>"][t]}}

(it's the solution of a system of ODEs that I obtain by discretizing a PDE with the method of lines). Now I would like to extract a particular value for each function, for example u_2[0.5] but I'm not managing to do that. Can someone help me?

Thank you so much!

Answer 1

A very simple working example:

n = 5;
T = 100;
U[t_] := Table[Subscript[u, i][t], {i, 0, n}];
eqns = Table[Derivative[1][Subscript[u, i]][t] == 0, {i, 0, n}];
initc = Table[Subscript[u, i][0] == 1, {i, 0, n}];
lines = NDSolve[{eqns, initc}, U[t], {t, 0, T}];

U[t] /. First@lines /. (t -> .5)

{1., 1., 1., 1., 1., 1.}

Alternatively:

vars = Table[Subscript[u, i], {i, 0, n}]
sol = NDSolve[{eqns, initc}, vars, {t, 0, T}]
#[t] & /@ vars /. First@lines /. (t -> .5)

{1., 1., 1., 1., 1., 1.}