Solving system of integral equations numerically - wolfram-mathematica

Question

Please, help me to understand...
Im solving system of equations
`f1[\[Lambda]1_, t_] := \[Lambda]1*Exp[-\[Lambda]1*t];
f2[\[Lambda]2_, t_] := \[Lambda]2*Exp[-\[Lambda]2*t];
f3[\[Lambda]3_, t_] := \[Lambda]3*Exp[-\[Lambda]3*t];
f4[\[Lambda]4_, t_] := \[Lambda]4*Exp[-\[Lambda]4*t];
f5[\[Lambda]5_, t_] := \[Lambda]5*Exp[-\[Lambda]5*t];
f6[\[Lambda]6_, t_] := \[Lambda]6*Exp[-\[Lambda]6*t];
f7[\[Lambda]7_, t_] := \[Lambda]7*Exp[-\[Lambda]7*t];
f8[\[Lambda]8_, t_] := \[Lambda]8*Exp[-\[Lambda]8*t];
f9[\[Lambda]9_, t_] := \[Lambda]9*Exp[-\[Lambda]9*t];
f10[\[Lambda]10_, t_] := \[Lambda]10*Exp[-\[Lambda]10*t];`
`p = ( {
{0, 1, 0, 0, 0, 0, 0},
{0, 0, 1, 0, 0, 0, 0},
{0, 0.3, 0, 0.6, 0.1, 0, 0},
{0, 0.4, 0, 0, 0.1, 0.5, 0},
{0, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0}
} );`
`fun[t_] := ( {
{0, f1[1/6, t], 0, 0, 0, 0, 0},
{0, 0, f2[1/2, t], 0, 0, 0, 0},
{0, f6[1/1, t], 0, f4[1/1, t], f3[1/1, t], 0, 0},
{0, f7[1/5, t], 0, 0, f5[1/2, t], f8[1/8, t], 0},
{0, 0, 0, 0, 0, 0, f9[1, t]},
{0, 0, 0, 0, 0, 0, f10[1, t]},
{0, 0, 0, 0, 0, 0, 0}
} );`
`T := 0.01;
q[t_] := p*fun[t];
q[t] // MatrixForm
r[n_] := Table[
q[n*T][[k, j]] +
Sum[Sum[T*q[n*T - i*T][[m, j]]*Subscript[\[Phi], m][i*T], {i, 0,
n}], {m, 1, 7}], {j, 1, 7}, {k, 1}];
r[1] // MatrixForm
aa[n_] :=
Table[Subscript[\[Phi], j][n*T] == r[n][[j, 1]], {j, 1, 7}];
bb[n_] := Table[Subscript[\[Phi], j][n*T], {j, 1, 7}];`
Sol[n_] := Solve[aa[n], bb[n]] /. Solve[aa[n - 1], bb[n - 1]];
Sol[1] // MatrixForm
I have values for Sol[0] and Sol[1], but for Sol[2], Sol[3], etc. Mathematica don't substitute previous values...
`
I solved this system in Laplace domain. I tried to obtain the values in range from 0 to 50.