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[MUG] Re: Coupled, nonlinear ODEs.
| [MUG] Re: Coupled, nonlinear ODEs. |
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Author: Robert Israel
Posted: Thu, 16 May 2002 13:28:07 -0700
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>> From: Robert Israel "israel"
Some nonlinear systems can be solved, but most will have no closed form
solutions. Maple 7 has so far spent 4450 CPU seconds on yours (on a Sun)
with no result yet, so I think I'll give up on it.
This autonomous 2 x 2 system can be reduced to a single DE for, say, y as
a function of x:
2
d b x (1 - y(x)) + (c x - d) y(x) (1 - y(x))
ode := -- y(x) = -------------------------------------------
dx 2
a - b x - (c x - d) y(x) (1 - y(x))
But it seems that either generating or analyzing the symmetries of this DE
may be a difficult task (or else I've encountered a bug in Maple).
Robert Israel "israel"
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
On Tue, 14 May 2002, Anders Ballestad wrote:
> I am trying to solve a set of coupled nonlinear ODEs, and have
> tried mostly a numerical approach so far (LSODA from LLNL); however, I'd
> like the analytical solutions, if possible. A simple version of the
> equations at hand are:
>
> dx/dt = a - b*x^2 - (c*x-d)*z
> dy/dt = b*x^2*(1-y) + (c*x-d)*z
>
> where
>
> z(t) = y*(1-y) and
> x = x(t), y=y(t), and the constants (a, b, c, d) are all constant.
>
> Another numerical snag here is the stiffness of this problem: a~1,
> b~c~10^10 and d~10^5.
>
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