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Re: NDSolve series of ode with equilibrium conditions

• To: mathgroup at smc.vnet.net
• Subject: [mg21901] Re: NDSolve series of ode with equilibrium conditions
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 4 Feb 2000 02:54:35 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <87avsu$o1r@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

your equilibrium conditions turn the equations form ordinary
differential equations to  differential-algebraic equations.
This is a dramatic change. 
a) solve the system with out the algebraic equations and keep
   your fingers crossed that the errors in the numerical solution
   violate your algebraic constrains not too strong. 
b) you can try to eliminate some of the differntial equations
   using your algebraic equations i. e. replacing y1[t] in all
   equations by K*y2[t]*y3[t] and solve the smaller system
c) you can use a solution algorithm for differential-algebraic equations
   but Mathematica has no build-in solver for differential-algebraic
equations
   and the standard method work only for index 1 -- index 3 systems and
   have typical no stepsize control because the step size adjustment
   destroy the preservation of your algebraic equations
   
If you choose the last variant, I can give you a nice symmetric
projection
method for index 1 systems.

Hope that helps
  Jens

David Grymonpre wrote:
> 
> I am having a problem using NDSolve.  I have a series of  linear ODE's
> such as:
> 
> y1'[t]== f(y1[t], y2[t], ...y40[t])
> .
> .
> .
> y40'[t]== f(y1[t], y2[t], ...y40[t])
> 
> with initial conditions for each equation.  I need to add several
> equilibrium equations where one variable is a function of several of the
> other variables such as:
> 
> y1[t]=K*y2[t]*y3[t]  where K is a constant.
> 
> As of now, the system is quite complex (as far as lines of code for the
> problem) and I am trying to find a way to include these equilibrium
> equations in my system.  The code works when the equilibrium equations
> are not included.  How do I include the additional equilibrium
> equations?  I am using version 3.0.
> 
> David Grymonpre
> 
> begin:vcard
> n:Grymonpré;David
> tel;fax:850-410-6150
> tel;work:850-410-6578
> x-mozilla-html:FALSE
> org:FAMU-FSU College of Engineering;Department of Chemical Engineering
> adr:;;2525 Pottsdamer St.;Tallahassee;FL;32310;
> version:2.1
> email;internet:grymonpr at eng.fsu.edu
> title:Adjunct Professor and Ph.D. Candidate
> fn:David Grymonpré
> end:vcard