Diff.eq. system: simple numerical solution vs difficult analitical one.
- To: mathgroup at smc.vnet.net
- Subject: [mg43335] Diff.eq. system: simple numerical solution vs difficult analitical one.
- From: "Alessandro Esposito" <theopps75 at yahoo.it>
- Date: Mon, 25 Aug 2003 04:10:46 -0400 (EDT)
- Organization: GWDG, Goettingen
- Sender: owner-wri-mathgroup at wolfram.com
I have a system of 9 diff.eq. but the first four are independent from the
others and could be represented by:
mat = {
{-kdex, kdf, 0, kaf},
{kdex, -kdf - kdb - ket, kaf, 0},
{0, 0, -kdf - kaf - kdb - kab, kdex},
{0, ket, kdf, -kaf - kdex - kab}
};
inicond={n1[0]==f0,n2[t]==0,n3[t]==0,n4[t]==0}
I don't post the complete system for simplicity.
So I wasn't able to retrieve the analytical solution and I got easier the
numerical one. For reliable physical parameter values kab and kdb are very
smaller than the others. The system represent transition between electronic
states of a photo-excitable molecule. In these conditions the numerical
solution of the system consists in four single exponential decay, with same
time constant but different preexponential factors.
I fitted these trying to get a relationship between the time constant,
prefactors and the ki.... unfortunately I was just able to get the
prefactors helped by the steady-state solution (kab and kdb null).
The difference of complication between the numerical solution and the
analytical originate from a firs transient that populate the four different
states at which the simple decay follows.
Do you have any suggestion from a mathematical point of use or in the use of
mathematica.
I read some post about MatrixExp but I don't get how to use eventually this
in my case.
Thanks!!! :)
Ale
theopps75 at yahoo.it
ENI.G