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