Re: RecurrenceTable can't finish
- To: mathgroup at smc.vnet.net
- Subject: [mg101502] Re: RecurrenceTable can't finish
- From: dh <dh at metrohm.com>
- Date: Thu, 9 Jul 2009 01:53:23 -0400 (EDT)
- References: <h27fgt$cpb$1@smc.vnet.net>
Hi Ian,
consider your first recurrence relation:a[i] ..==a[i] .. + d[i+1] a[i+1]
If i=n: d[i+1] becomes zero and the recursion fails.
Daniel
EcoTheory wrote:
> I have a RecurrenceTable that works for all but the last element, at which it stumbles across a ComplexInfinity that does not occur when I do the final calculation myself. Here is self-contained (if not explained) code. Runs fine when the nspec for RecurrenceTable is {i,1,n-1} (as below), but gives the error when nspec is {i,1,n}. I can use the recurrence equation to calculate the last value (for n) without problems, but RecurrenceTable can't.
>
> n = 20;
> Guess = 7*10^-5;
> b[i_] := Piecewise[{{0, i == 0 || i == n}}, 3/10];
> d[i_] := Piecewise[{{0, i == 0 || i == n + 1}}, 5/10 i/n];
>
> q = RecurrenceTable[{a[i] (1 - d[1] q1) ==
> b[i - 1] a[i - 1] + (1 - b[i] - d[i]) a[i] + d[i + 1] a[i + 1], q1 (1 - d[1] q1) == (1 - b[1] - d[1]) q1 + d[2] a[2], a[1] == Guess}, a, {i, 1, n-1}]];
>
> That the solution is right for a[1] through a[n-1] can be confirmed with the following code.
>
> k = 10; (* Initial Population Size *)
> p0 = Table[1/k! D[x^k, {x, i}], {i, 0, n}] /. x -> 0;
> P = Table[1/(j + 1)! D[b[j] x^(j + 1), {x, i}] + 1/(j - 1)! D[d[j] x^(j - 1), {x, i}] + 1/(j)! D[(1 - (b[j] + d[j])) x^j, {x, i}], {i, 0, n}, {j, 0, n}] /. x -> 0;
> p[t_] := MatrixPower[N[P], t, p0];
> qGood = p[5000][[2 ;; n + 1]]/(1 - p[5000][[1]]);
> Show[ListLinePlot[qGood], ListPlot[q]]
>
> Any suggestions? Thanks - Ian
>