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Question: pdsolve - boundary condition issues

Question:pdsolve - boundary condition issues

charlesreid1 12 Maple
pde pdsolve
March 01 2008
0
Hi - I'm trying to solve a PDE using pdsolve() for the Graetz problem (heat transfer in a pipe). I can solve the PDE and get a general solution, but when I try to solve the equation with the boundary conditions, Maple thinks that the boundary conditions are new functions with the same name. Here is how I am doing it now: > heat := (1-z^2)*(diff(T(y, z), y)) = (diff(z*(diff(T(y, z), z)), z))/z; > cond := T(0, z) = 0, T(y, 1) = 1, diff(T(y, 0), z) = 0; > PDE := [heat, cond]; > sol := pdsolve(PDE, T(y, z)); This throws the error: Error, (in pdsolve/sys/info) found functions with same name but depending on different arguments in the given DE system: {T(y, z), T(0, z), T(y, 1)} I've also tried: > heat := (1-z^2)*(diff(T(y, z), y)) = (diff(z*(diff(T(y, z), z)), z))/z; > cond := T(0, z) = 0, T(y, 1) = 1, diff(T(y, 0), z) = 0; > sol := pdsolve(heat, T(y, z), cond) Which throws a different error: Error, (in pdsolve/info) wrong extra arguments: {0 = 0, T(0, z) = 0, T(y, 1) = 1} I have seen an example that successfully uses the former method (http://www.math.uic.edu/~jan/mcs494f02/Lec34/pde1.html), but copying & pasting the example verbatim gives the same error. The Maple Documentation/Help file for pdsolve() doesn't explain how to implement boundary or initial conditions at all. Can someone help me out here? chz
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