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MathGroup Archive 2000

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two variable recurrence relations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24448] two variable recurrence relations
  • From: "Rajgopal Kannan" <rkannan at cs.uah.edu>
  • Date: Tue, 18 Jul 2000 00:58:50 -0400 (EDT)
  • Organization: The University of Alabama in Huntsville
  • Sender: owner-wri-mathgroup at wolfram.com

The mathematica manual I checked doesn't say anything about two variable
recurrence relations. I would like to know whether one can use mathematica
to solve non-linear recurrence relations in two variables for example, the
system of relations  below:

Calculate { X_{iq} }, { Y_{iq} }, { Z_{ijq} }, (non-integral
values allowed), 0 <= i,q <= n where,
 X_{iq} + Y_{iq} <= 1
Z_{ijq} + Z_{iqj} <= 1
A_i - C_{ij} <= .5
such that
E_i = \sum_q ( D_{iq} X_{iq} )
F_i = \sum_q ( D_{iq} Y_{iq} )
A_i = E_i  + ( B_i + F_i ) A_{i-1}
C_{ij} = ( B_i Y_{ij} + G_{ij} ) + (B_i X_{ij} + F_{ij} ) C_{i-1,j-1}
B_{i-1} = 2 B_i (1 - E_i)

etc. etc. along with appropriate boundary conditions.

The series for A_i and C_ij can be easily simplified but the terms are of
course
higher order and non-linear in X,Y,Z.
Is there something that can be done to solve this system of equations?
I would appreciate any help.
Thanks.
Raj.






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