The output of Mathematica is only a copy of the input. What am I doing wrong?
RSolve[r1[(n + 1)*t] == 1/2 (r1[n*t] +
r4[n*t] + (r1[n*t] - r4[n*t]) Cosh[
2 (-1 + n)* t] + (-r2[n*t] + r3[n*t]) Sinh[2 t - 2 n *t]),r2[(n + 1)*t] == 1/2 (r2[n*t] + r3[n*t] + (r2[n*t] - r3[n*t]) Cosh[
2 (-1 + n) *t] + (-r1[n*t] + r4[n*t]) Sinh[2 t - 2 n* t]), r3[(n + 1)*t] == 1/2 (r2[n*t] +
r3[n*t] + (-r2[n*t] + r3[n*t]) Cosh[
2 (-1 + n)* t] + (r1[n*t] - r4[n*t]) Sinh[2 t - 2 n *t]), r4[(n + 1)*t] == 1/2 (r1[n*t] + r4[n*t] + (-r1[n*t] + r4[n*t]) Cosh[2 (-1 + n) *t] + (r2[n*t] - r3[n*t]) Sinh[2 t - 2 n *t]), r1[0] == 1, r2[0] == r3[0] == r4[0] == 0}, {r1[n], r2[n], r3[n], r4[n]}, n ]
t=1
and you remove all your hyperbolic trig functions then Mathematica is able to find a solution. Skip either of those steps and it cannot find a way to get a solution $\endgroup$ – Bill Sep 21 at 17:39