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MathGroup Archive 1997

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Yikes! More PDE questions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7017] Yikes! More PDE questions
  • From: "Rick A. Sprague" <sprague at egr.msu.edu>
  • Date: Fri, 2 May 1997 21:30:45 -0400 (EDT)
  • Organization: Michigan State University College of Chemical Engineering
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

Can somebody show me an example of solving a system of PDE's using NDSolve?
 I have had ZERO luck solving any PDE's  beyond the examples in the MMA
help file. I'm not interested in variations in the elliptic, parabolic,
wave, etc. equations - I know that these can be solved - may be that's why
they're in the help file!   Why can't MMA numerically solve the following
problem.  The MMA help file says it can solve system of inital value PDE's.
 In what context can it numerically solve PDE's?   This is my problem:

dX[z,t]/dz=Q[z,t]-X[z,t]
dQ[z,t]/dt=X[z,t]-Q[z,t]

BC:
X[0,t]==1;
Q[z,0]==0;

Both derivatives are partials.

I can understand MMA can't solve this problem analytically.  FYI, a book
has the analytical solution, it is found by using laplace transforms:

X(z,t) = 1 - NIntegrate[Exp[-zd-t]BesselJ[0,I Sqrt[4zd t],{zd,0,z}]

MMA choked on the Laplace inversion.  I have a variation to this problem
and must resort to solving these equations numerically(I have done so
already w/C++).  

This is what I entered to solve it numerically in MMA:

IN:	NDSolve[{D[X[z,t],z]==Q[z,t]-X[z,t],D[Q[z,t],t]==X[z,t]-
Q[z,t],Q[z,0]==0,X[0,t]==1},{X,Q},{t,0,10},{z,0,10}]

	NDSolve::pde: Built-in routines cannot solve the partial differential
equation


Thanks,

Rick Sprague


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