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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?

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  • 2
    $\begingroup$ "Why doesn't Mathematica solve this?" - possibly because the closed form (if it does have one) is not necessarily known to Mathematica. $\endgroup$ – J. M. is away Apr 13 '17 at 10:16
  • $\begingroup$ "partical"????? $\endgroup$ – David G. Stork Apr 13 '17 at 17:32
  • $\begingroup$ "partial"**, sorry. $\endgroup$ – user56834 Apr 14 '17 at 8:36
  • $\begingroup$ I see. I did not know that RSolve necessarily calculated a closed form solution. That solves it. $\endgroup$ – user56834 Apr 14 '17 at 8:37
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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

enter image description here

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