Question: System of coupled PDEs

Hi,

I would like to solve the system of PDEs

PDE1 := diff(a(x,t),t) = - 2*a(x,t) + 1*b(x,t)
- 4*( diff(a(x,t),x,x) + a(x,t)*diff(b(x,t),x,x) - b(x,t)*diff(a(x,t),x,x) );

PDE2 := diff(b(x,t),t) = - 1*b(x,t) + 2*a(x,t)
- 4*( diff(b(x,t),x,x) - a(x,t)*diff(b(x,t),x,x) + b(x,t)*diff(a(x,t),x,x) );

subjected to the initial value

IC := [ a(x,0)=exp( (x-0.5)^2 ), b(x,0)=0 ];

If I try to do so by typing

pdsolve([PDE1,PDE2],IC,numeric);

Maple prints

Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable

Does this mean that Maple needs also boundary conditions to solve it? Since I do not have this information (this PDE approximates a stochastic process and I know just the starting values), is there any possiblity to solve it using a different method? If not, is there any other software which could do this job? (The only additional information I could give is 0 \leq x \leq 1, but Maple seems not to be interested in this one ...)

Out of curiosity: what is the technical reason for the need of a boundary condition? I am asking, because the above PDE system approximates a very large ODE system. Indeed, the stochastic process was initially approximated by a first order ODE system, where each ODE encoded in essence a position on the unit interval. But for the solution of such an ODE an initial condition is all we need.

It would be great if someone could help.

Greetings,

Herlod