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.