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
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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