Solving a system of equations without having to define exact

*To*: mathgroup at smc.vnet.net*Subject*: [mg112528] Solving a system of equations without having to define exact*From*: "Michael A. Gilchrist" <mikeg at utk.edu>*Date*: Sat, 18 Sep 2010 07:27:44 -0400 (EDT)

Hi, I'm working with a model that consists of a series of coupled ODEs and I am trying to study their equilibrium behavior. Below is the code I use to define the equations and solve for the equilibrium state. (*-----------------------------------------------------*) (*define the variables *) imax = 3; valsI = Table[m[i], {i, 0, imax}]; valsII = Table[ms[i], {i, 0, imax}]; (*generate the equations *) eqnsI = Join[{lambda + t m[1] - (k + mu) m[0]}, Table[k m[i - 1] - km[i] + t (m[i + 1] (i + 1) - m[i] i ) - mu m[i], {i, imax}] /. {m[imax + 1] -> 0}] ; eqnsII = Join[{mu m[0] + t ms[1] - delta ms[0]}, Table[ t (ms[i + 1] (i + 1) - ms[i] i ) + mu m[i], {i, imax}] /. {ms[imax + 1] -> 0}] ; (*solve the equation *) sol = Solve[Map[0 == # &, Join[eqnsI, eqnsII]], Join[valsI, valsII]]// Simplify; (*------------------------------------------------*) If I set imax to a small integer value such as 2 to 8, Mathematica crunches out a solution quickly. As imax gets bigger, Mathematica still comes up with a solution, but it gets ever more complex and difficult to calculate. Based on this behavior, I surmise there is a general solution to these equations but it is sufficiently complex that I cannot intuit it from looking at the solutions with imax = 2, 3, 4, .... I would love it if I could get Mathematica to give me a general solution such that the variable imax does not need to be explicitly defined. Does anyone know of a way to pose such a problem (i.e. solve a set of equations where the exact number is unspecified) to Mathematica? Or is this impossible? Any help would be greatly appreciated. Thanks for your attention to this matter. Mike