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 ftp://amath-www.colorado.edu/pub/mathsym Unfortunately, it can not handle your example yet because it doesn't know that y[t] is Derivative[0][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 sherod at newton.colorado.edu 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[14]= |> {{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, |> |> Adam |> |> ----- |> 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 |> |> |> ==== [MESSAGE SEPARATOR] ====