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Re: Multiple St.St. and Alg-Diff Eq

• To: mathgroup at smc.vnet.net
• Subject: [mg23115] Re: Multiple St.St. and Alg-Diff Eq
• From: Eckhard Hennig <hennig at itwm.uni-kl.de>
• Date: Wed, 19 Apr 2000 02:30:47 -0400 (EDT)
• Organization: ITWM
• References: <8d9758$iih@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Sharon Smith schrieb in Nachricht <8d9758$iih at smc.vnet.net>...
>Two questions:
>
>1) Can Mathematica solve for multiple steady states?  Currently I am using
>Findroot and am getting solutions seem to oscillate between 2 different
>steady states.


Sharon,

since you mentioned the function FindRoot, I assume that what you are
referring to is the initial solution of a set of differential equations at t
= 0 or, in terms of circuit analysis, the DC operating point. The term
"(periodic) steady state" usually refers to the response of a system to a
(periodic) input signal as t approaches infinity, that is after all
influences of initial conditions have vanished.

OK, back to your question: If you encounter oscillations when trying to find
a DC OP using FindRoot, you can try the following.

* play with the FindRoot option DampingFactor
* try different initial values (for instance, by adding random noise)
* use the secant method instead of the Newton-Raphson method

However, there is no guarantee that the above approaches will be successful.

>2) Can Mathematica solve systems of Algebraic and Differential Equations
>(i.e. like DASSL)?


No, not in the general case. If you need a DAE solver, you may want to try
the package NDAESolve which is part of the circuit analysis toolbox Analog
Insydes. There's a free demo version available from
www.itwm.uni-kl.de/as/products/ai or from MathSource.

Best regards,

  Eckhard

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Dr.-Ing. Eckhard Hennig        mailto:hennig at itwm.uni-kl.de
Institut fuer Techno- und Wirtschaftsmathematik e.V. (ITWM)
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  Voice: +49-(0)631-205-3126    Fax: +49-(0)631-205-4139
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     ITWM - Makers of Analog Insydes for Mathematica
        http://www.itwm.uni-kl.de/as/products/ai
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