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 == GC == 0 GC' == 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.