Hello everyone
I am trying to plot u(t) and v(t) vs t but no luck. I have also used RecurrenceTable but of no use.
Here are the couple funtions
u[0] = 0.5; alpha = 1/2; t1 = 2; l = 20; v[0] = 0.5;

u[t_] := Piecewise[{{u[0] +
Integrate[(u[t/2] + Cos[v[t/2]])/(t^3 + 100), {t, 0, t1}],
0 <= x <= t1}, {u[1] +
Integrate[(u[t/2] + 1/Sqrt[alpha]*Cos[v[t/2]])/(t^3 + 100), {t,
t1, t}], t1 <= x <= l}}]

u[t_] := Piecewise[{{v[0] +
Integrate[(v[t/2] + Sin[v[t/2]])/(t^5 + 100), {t, 0, t1}],
0 <= x <= t1}, {v[1] +