How to solve this coupled recurrence eqation?
- To: mathgroup at smc.vnet.net
- Subject: [mg40435] How to solve this coupled recurrence eqation?
- From: Peter W <pewei at algonet.se>
- Date: Sat, 5 Apr 2003 04:00:05 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I tried RSolve on this system of coupled recurence equations with
not so good result, maybe there are some tricks?
eqs = {
r[1][p + 1] == 0.3628 r[1][p] + 0.1360 r[3][p] + 0.59648 r[4][p]
+ 2.4838 r[5][p] + 5.4 r[6][p],
r[2][p + 1] == 0.2763 r[1][p] + 0.3332 r[2][p] + 0.0529 r[3][p]
+ 0.23196 r[4][p] + 0.96592 r[5][p] + 2.1 r[6][p],
r[3][p + 1] == 0.0607 r[1][p] + 0.3124 r[2][p] + 0.3937
r[3][p],
r[4][p + 1] == 0.0542 r[2][p] + 0.266 r[3][p] + 0.4150 r[4][p],
r[5][p + 1] == 0.0402 r[3][p] + 0.225 r[4][p] + 0.2778 r[5][p],
r[6][p + 1] == 0.05957 r[4][p] + 0.1631 r[5][p]
};
start values e.g.:
{
r[1][0] ==800,
r[2][0] == 200,
r[3][0] == 500,
r[4][0] ==1200,
r[5][0] ==400,
r[6][0] == 400}
This is what I plugged into RSolve (I tried startvalues: numerical, as
undetermined constants (as below), and no staringvalues at all).
RSolve seems to determine the system " RowReduce::"luc": "Result for
RowReduce of badly conditioned matrix " " etc....
sol = RSolve[Flatten[Join[eqs, {
r[1][0] == c1,
r[2][0] == c2,
r[3][0] == c3,
r[4][0] == c4,
r[5][0] == c5,
r[6][0] == c6}]], {r[1], r[2], r[3], r[4], r[5], r[6]}, p]
With no starting values I got some result that not seem to agree with
step by step calculation of the system.
The reason I look for closed solution is that I want to estabish the
symptotic behavior for the system for different numerical coefs. in eqs.
Best regards Peter W