Question: Solving a system of one PDE and one ODE

Dear All,

This's my first post on this website; I'm hoping I can get some useful ideas on how to approach a problem where a PDE is coupled with an ODE, with initial and boundary conditions.  I'm using Maple 12.

The PDE is,

PDE:=diff(g(x,t),t)=diff(g(x,t),x$2)

the ODE is,

ODE:=diff(f(t),t)=g(1,t)-f(t)

The initial and boundary conditions are,

IBC:={g(x,0)=0,f(0)=.2,D[1](g)(0,t)=0,D[1](g)(1,t)=-g(1,t)+f(t)

I'm trying to solve and plot,

sys:={PDE,ODE}

sol:=pdsolve(sys,IBC,[g,f],numeric,time=t,range=0..1)

p1:=sol:-plot(t=10,numpoints=50,color=red)

p2:=sol;-plot(t=30,numpoints=50,color=blue)

plots[display]({p1,p2})

but i'm getting an error; it seems like it's not liking g(1,t); it can do it if the ODE was a PDE, i. e.,  f(x,t).  Has anyone done a similar problem?

Thanks in advance

J. Lynn