[Date Index]
[Thread Index]
[Author Index]
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
Prev by Date:
**Re: Solving differential equations?**
Next by Date:
**Re: New Version 3 Presentations**
Previous by thread:
**Re: Problem with Run[]**
Next by thread:
**Category Theory with Mathematica**
| |