Author 
Comment/Response 
Tim Mc

10/26/08 10:48pm
I have a system of PDEs I am looking to solve using NDSolve. (This is a simple version of the system with the constants removed, I can provide the full set if need be, but the general mathematical form is the same). The text I enter into Mathematica is listed below:
solution = {X, A, G, F, H} /. First[
NDSolve[
{D[X[z, t], t] +
D[X[z, t], z] == (1  2 X[z, t])*(A[z, t] + G[z, t]) 
X[z, t] + (1  2 X[z, t])*(F[z, t] + H[z, t]),
D[A[z, t], t] + D[A[z, t], z] == (1  2 X[z, t])*A[z, t] 
A[z, t],
D[G[z, t], t]  D[G[z, t], z] == (1  2 X[z, t])*G[z, t] 
G[z, t],
D[F[z, t], t] D[F[z, t], z] == (2 X[z, t]  1)*F[z, t] 
F[z, t] + 2 X[z, t],
D[H[z, t], t]  D[H[z, t], z] == (2 X[z, t]  1)*H[z, t] 
H[z, t] + 2 X[z, t],
X[z, 0] == 0,
A[0, t] == 20,
G[10, t] == 20,
F[0, t] == 0.1,
H[10, t] == 0},
{X, A, G, F, H},
{z, 0, 10},
{t, 0, 1}]]
When I enter the text I receive the following error message:
NDSolve::ivone: Boundary values may only be specified for one \independent variable. Initial values may only be specified at one \value of the other independent variable. >>
Am I doing something fundamentally wrong with my code or setup/typing or is my system of equations simply not solvable with NDSolve?
If so are there any suggestions on how I might solve this? Finite Difference methods?
Thanks in Advance,
Tim
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