Re: not linear homogeneus differential equation system... too complicated for mathmeatica... maybe only for me! :)
- To: mathgroup at smc.vnet.net
- Subject: [mg41729] Re: [mg41718] not linear homogeneus differential equation system... too complicated for mathmeatica... maybe only for me! :)
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Tue, 3 Jun 2003 07:13:11 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Monday, June 2, 2003, at 04:35 AM, Alessandro wrote:
> For the type of system I'm studing I guess the system of differential
> equation (not liear) I'm going to asking about should have solution.
> Unfortunatly my knoledge about mathmatica is very poor, seems to be a
> bit
> too complicated to try with paper and pencil in a reasoneble time, and
> so
> I'd like to have some help.
> The Mathematica cell is:
>
>
> DSolve[
> { s'[t] == -A*s[t] +B*u[t],
> u'[t] == A*s[t] - (E + C*a[t] + B)*u[t],
> a'[t] == F*b[t] - C*a[t]*u[t],
> b'[t] == C*a[t]*u[t] - (G + F)*b[t],
> s[0] == s0, a[0] == a0, b[0] == 0, u[0] == 0},
> {s[t], u[t], a[t], b[t]}, t]
>
> I have two problem:
> 1) Before I was considering C=C' 1/a[t]... the system was linear and
> solvable. Nevertheless the solution was a very long formula. I needed
> to
> compact the result with FullSimplify. Is it the right way or I can feed
> DSolve with some option in order to get a compact result by default?
DSolve followed by Simplify or FullSimplify is probably the right thing
to do.
> 2) Later I realized I was solving the erroneous equations. This new
> non
> linear system is solved by Mathematica, after some minutes (CPU 2GHz
> 512Mb),
> Mathematica answer with the same input I gave as output... well... I
> think
> it is not able to solve it. There is some mathematica toolbox or some
> way to
> solve it. It is probable I wiil need to change other things in the
> equation
> so I'd prefer some suggestion in order to understand what to do
> instead of
> the raw solution... however I will not disregard a solution :))))
You'll have to settle for a numerical solution using NDSolve. Of course
this will require specific values for the coefficients.
-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis