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MathGroup Archive 1997

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Re: system of non-linear ODEs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6409] Re: [mg6394] system of non-linear ODEs
  • From: seanross at worldnet.att.net
  • Date: Tue, 18 Mar 1997 22:16:09 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

scd at gopher.chem.wayne.edu wrote:
> 
> Hi !
> 
> Does anyone know how to solve non-linear ODE systems like
> 
> GP ' [t] ==   a  - b GC[t] - c GP[t]  - GC' [t]
> GC'[t] == d GP[t] GM[t] / (e + f GM[t] )
> 
> a,b,c,d,e  constants
> 
> with the initial conditions :
> 
> GP[0] == GC[0] == 0   GC' [0]== 0
> 
> where GM[t] can be either a constant, GP[t] or a function of GP[t] and
> GC[t]?
> 
> Mathematica DSolve bounces it back in the case GM[t] == GP[t]  and
> upper
> 
> Why ? How to solve that ?
> 
> Thanks a lot
> 
> scd at gopher.chem.wayne.edu


It looks like you are attempting to use mathematica to make up for a 
lack of knowledge of basic numerical techniques.  This is a big mistake 
and will eventually lead to garbage answers.  I recommend you go by your 
local college bookstore and buy a book on numerical analysis or get a 
copy of "numerical recipes". Look up the various Runga-Kutta methods for 
solving differential equations.  They are usually stated in the 
textbooks in terms of linear ODE's, but can be applied to non-linear and 
to coupled systems just as well.  Mathematica is a full-blown 
programming language, not just a collection of nifty functions.  Any 
number crunching(numerical analysis) that can be done in C or Fortran 
can, in my opinion, be done more conveniently in mathematica.


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