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MathGroup Archive 1999

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NDSolve - large ODE systems

  • To: mathgroup at smc.vnet.net
  • Subject: [mg17953] NDSolve - large ODE systems
  • From: "Bernd Kaestner" <b.kaestner1 at physics.ox.ac.uk>
  • Date: Mon, 7 Jun 1999 02:51:15 -0400
  • Organization: Oxford University, England
  • Sender: owner-wri-mathgroup at wolfram.com

Hallo everyone,

I would be really glad if anybody could comment on the following problem. I
am trying to solve a large system of first order nonlinear differential
equations. The system consists of about 100 000 equations and involves power
up to third order in the coupled functions. Is there any hope to solve such
a problem on a PC using Mathematica?

It is possible to formulate the problem as 5 coupled partial differential
equations (this is actually the original equation, from which a
discretisation gave the above ODE system). The 5 functions depend on three
variables. In order to solve this I tryed:

sol=NDSolve[
 {D[u[x,t],t]==D[v[x,t],x,x]+v[x,t](u[x,t]^2+v[x,t]^2)+u[x,t] uv[x,x,t],
  D[v[x,t],t]==D[u[x,t],x,x]-u[x,t](u[x,t]^2+v[x,t]^2)-v[x,t] uv[x,x,t],
  D[uv[x,y,t],t]==uv[x,y,t](u[x,t]v[x,t]+uv[x,x,t]-u[y,t]v[y,t]-uv[y,y,t]),
  D[uu[x,y,t],t]==...,
  D[vv[x,y,t],t]==...,
   u[x,0]==Sech[x/0.05],
   v[x,0]==0,
   u[-5,t]==0,
   u[5,t]==0,
   v[-5,t]==0,
   v[5,t]==0,
   uv[x,y,0]==0,
   uv[-5,y,t]==0,
   uv[5,y,t]==0,
   uv[x,-5,t]==0,
   uv[x,5,t]==0,
   ...
  },
 {u,v,uv,uu,vv},{x,-5,5},{y,-5,5},{t,0,1}]

However, mathematica expects only two independend variables:

NDSolve::"nonopt":
    "Options expected (instead of {t, 0, 1} beyond position ... in ... An
option must be a rule or a list of rules."

Does anybody know if one can solve a PDE-system with three independend
variables with mathematica? If anybody knows of packages, which support
problems like this, please let me know.

Thank you for your help,
Bernd




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