coupled eqns in NDSolve

[Stergios J. Papadakis]

Dear group,
Do you know if NDSolve can solve two coupled equations with
different numbers of variables? It looks to me like the algorithm
should be able to do so, but that there is some test beforehand
that doesn't let it start (it just returns a message that
"the length of the derivative operator... is not the same as
the number of arguments"). Do you think I just have the
syntax wrong or can NDSolve not do this?

I am trying to solve 2 coupled differential equations
using NDSolve. One is a function of time t only, z[t] (the
harmonic oscillator equation) and the other is a function
of position x and time t, T[x,t] (the heat equation). They are
coupled because the harmonic oscillator solution z[t]
is a boundary condition on the heat equation, and the
heat equation solution at one particular location L on the
boundary, T[L,t], modifies the spring constant of the harmonic
oscillator equation.

I got NDSolve to work by artificially making z a function
of x and t (z[x,t]), knowing that only z[L,t] really had any
meaning for me. However, this takes much longer than I think
it needs to because it is solving for z[x,t] everywhere along
x when it doesn't really need to. I ignore everything except
z[L,t] anyway.

What are your thoughts?
Thanks,
Stergios