n-dimensional recursion [closed]

Question

I am trying to set up a recursive function that generates n number of differential equations for Subscript[y, n][t]

This function almost works.

Table[{Subscript[y0, j] = 1}, {j, 50}];(*initial conditions for Subscript[y, n] assuming n<=50*)
vars[n_] := {x, Table[Subscript[y, j], {j, n}]};
sol[0][T_, b_, d_, r_, n_] := 
 sol[0][T, b, d, r, n] = 
  Flatten[vars[n]] /. 
   NDSolve[Flatten@{Join[{x'[t] == 
          10^7 r - d x[t] - b*x[t]*(Sum[Subscript[y, k][t], {k, n}])},
         Table[Subscript[y, j]'[t] == -d Subscript[y, j][t] + 
           b x[t]*Subscript[y, j][t], {j, n}], 
        Flatten[Join[{x[0] == 0}, 
          Flatten[Table[{Subscript[y, j][0] == Subscript[y0, j]}, {j, 
             n}]]]]]}, Flatten[vars[n]], {t, 0, T}][[1]]
sol[i][T_, b_, d_, r_, n_] := 
 sol[i][T, b, d, r, n] = 
  Flatten[vars[n]] /. 
   NDSolve[Flatten@{Join[{x'[t] == 
          10^7 r - d x[t] - b*x[t]*(Sum[Subscript[y, k][t], {k, n}])},
         Table[Subscript[y, j]'[t] == -d Subscript[y, j][t] + 
           b x[t]*Subscript[y, j][t], {j, n}], 
        Flatten[Join[{x[0] == 0},(*next bit seems to be the problem*)
          Flatten[Table[{Subscript[y, j][0] == 
              sol[i - 1][T, b, d, r, n][[j + 1]][T]}, {j, n}]]]]]}, 
     Flatten[vars[n]], {t, 0, T}][[1]]

The initial condition sol[0][T, b, d, r, n] works as expected and returns the interpolating functions:

T = 4; b = 10^-7; d = 0.25; r = 0.2; n = 4;
sol[0][T, b, d, r, n] 

And also returns the value at t = T e.g. sol[0][T, b, d, r, n][[2]][4]

sol[i][T, b, d, r, n] does not work for i>0.

It seems that the problem is where the solution from the previous iteration i-1 is used to set the initial conditions for current iterate i, as marked in the code.

I imagine this will be trivial to troubleshoot for someone on here. Any advice is much appreciated.

Answer 1

Very small error, but posting this as an answer so the question can be marked as resolved:

In defining the recursive version of sol, you wrote sol[i][T_, b_, d_, r_, n_] := (...) instead of sol[i_][T_, b_, d_, r_, n_] := (...)! That is, adding an underscore to that first occurrence of i seems to fix it.