Re: HELP! Why are the solutions from NDSolve and DSolve not identical?
- To: mathgroup at smc.vnet.net
- Subject: [mg37762] Re: HELP! Why are the solutions from NDSolve and DSolve not identical?
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Tue, 12 Nov 2002 03:13:11 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <aqnvtj$fot$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
NDSolve[] gives a numerical approximation to the solution.
DSovel[] give the solution of the differential equation.
An approximation must be different from the true solution
otherwise it is not a approximation.
As long as you don't give the full input, i.e., the paramters
a,b,c,d we can't tell you what's wrong with your numerical
solution and why it differs so much from the analytical
solution.
Regards
Jens
Loling Song wrote:
>
> I have, what I believe, a system of two linear, first-order,
> inhomogeneous differential equations describing a real biological
> system. When I tried to solve this system for a numerical solution by
> NDSolve, it gave a solution that was different from that of the
> symbolic solution (in which I used the same boundary conditions).
>
> NDSolve[{y1'[t] == a y1[t] + b y2[t], y2'[t] == d + c y1[t] - b y2[t],
> y1[0] == 0.0018, y2[0] == 0.03}, {y1[t], y2[t]}, {t, 0, 18000},
> MaxSteps -> 1000000, AccuracyGoal -> 10, PrecisionGoal -> 10,
> WorkingPrecision -> 20]
>
> DSolve[{y1'[t] == a y1[t] + b y2[t] , y2'[t] == d + c y1[t] - b y2[t]
> }, {y1[t], y2[t]}, t]
>
> I am puzzled by these results, and would very much like to arrive at an
> analytical solution. I would very much appreciate ideas and
> suggestions to help me get there.
>
> Many thanks in advance.
>
> Loling Song
> Cornell University
> Department of Physics,
> 117 Clark Hall,
> Ithaca, NY 14853
>
> Email: LS99 at cornell.edu