# Why doesn't this simple partial recurrence equation work in mathematica?

I have the following recurrence equation:

L[t_, alpha_] :=
Min[2*epsilon[t, alpha] - x[t, alpha], x[t, alpha - 1]]

epsilon[t_, alpha_] := alpha^2

d[t_] := 10

f = 10

RSolve[{x[t, alpha] == x[t - 1, alpha] + L[t - 1, alpha] - L[t - 1, alpha + 1],
x[0, alpha] == 0,
x[t, f] == x[t - 1, f] + L[t - 1, f] - d[t - 1]},
x[t, alpha], {t, alpha}]


It simply outputs the code from RSolve[... onwards, without giving any errors.

I cannot figure out what I am doing wrong: I'm giving an initial condition:

x[0, alpha] == 0


and a boundary condition on alpha:

x[t, f] == x[t - 1, f] + L[t - 1, f] - d[t - 1]}


Why doesn't mathematica solve this?

• "Why doesn't Mathematica solve this?" - possibly because the closed form (if it does have one) is not necessarily known to Mathematica. Apr 13, 2017 at 10:16
• "partical"????? Apr 13, 2017 at 17:32
• "partial"**, sorry. Apr 14, 2017 at 8:36
• I see. I did not know that RSolve necessarily calculated a closed form solution. That solves it. Apr 14, 2017 at 8:37

## 1 Answer

if you just want values you don't need RSolve

epsilon[t_, alpha_] = alpha^2
L[t_, alpha_] :=
Min[2*epsilon[t, alpha] - x[t, alpha], x[t, alpha - 1]]
f = 10
x[0, alpha_] = 0
d[t_] = 10
x[t_, f] := x[t - 1, f] + L[t - 1, f] - d[t - 1]
x[t_, alpha_] :=
x[t - 1, alpha] + L[t - 1, alpha] - L[t - 1, alpha + 1]
Table[ x[t, a] , {t, 0, 5}, {a, 15}] // MatrixForm