       Re: Solving sets of differential equations -- this should be easy...

• To: mathgroup at smc.vnet.net
• Subject: [mg3364] Re: Solving sets of differential equations -- this should be easy...
• From: sherod at boussinesq.Colorado.EDU (Scott Herod)
• Date: Sat, 2 Mar 1996 04:12:45 -0500
• Organization: University of Colorado at Boulder
• Sender: owner-wri-mathgroup at wolfram.com

```Depending on how general your sets of equations are, this is actually a
very hard problem.  The technique of choice appears to be a generalization
of ideas of Groebner Bases to systems of differential equations.  Currently
the only code in Mathematica that I am aware of which can begin to handle
general systems of linear pde's is part of the MathSym package available at

Unfortunately, it can not handle your example yet because it doesn't
know that y[t] is Derivative[y][t].

There are a couple of packages in Maple that can do systems of nonlinear
partial differential equations.  One is by Liz Mansfield and another by
Greg Reid, et al.  Likely there are more that I am unaware of.

As a side note, in one sense your system below is completely solved.  It
depends on how you choose to sort your functions.  From the way you have
them listed, it is back-substitution problem.

Scott Herod
Applied Math
University of Colorado, Boulder

In article <4h139q\$rr4 at dragonfly.wolfram.com>, axf at HPP.Stanford.EDU (Adam Farquhar) writes:
|>
|> I have what should be a very simple problem, but I can't convince
|> Mathematica to give me an answer in the form that I need.  I have sets
|> of equations like
|>
|> 	{x[t] == y'[t], y[t] == 5}
|>
|> that I would like to solve.  If I try the obvious
|>
|> 	DSolve[{x[t] == y'[t], y[t] == 5},x[t],t]
|>
|> I get
|> 	Out=
|> 		{{x[t] -> y'[t]}}
|>
|> as the result.  I would like, of course, to see {{x[t] -> 0}}. How can I
|> get Mathematica to give me this answer?
|>
|> The equations are being generated automatically, and Mathematica is being
|> called remotely.  The solution should be in the form of a single
|> self-contained request with no side-effects.
|>
|> Many thanks for your help,
|>
|>
|> -----
|> Dr. Adam Farquhar
|> Knowledge Systems Lab         URL: www-ksl.stanford.edu/people/axf
|> Gates Bldg 2A MC9020	      Email: afarquhar at ksl.stanford.edu
|> Stanford University	      Tel:   415-723-9770
|> Stanford, CA 94305            Fax:   415-725-5850
|>
|>
|>

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