ok i have re-jigged the code and i am now getting the same error as you mentioned, the error mentions that it has received several Float(undefined), which if i understand what your code is doing this shouldn't happen as the Float(undefined) should have been replaced by 0's. I don't know if you know any way round this.

With the Float(undefined)'s arising from the differentiation of the piecewise function is there away around this, maybe using if statements, i've not used if statements in maple before will it be able to handle a changing R in order to return the correct formula from the piecewise function?

ok, using your suggestions we appear to get a different error, our code will process through until the plot routine is called at which point i get the error, "Error, (in pdsolve/numeric/plot) unable to compute solution for t>0.:matrix is singular" not really sure how to go forward with this, i find it wierd that we are getting different errors.

i have entered values for H and a but that doesn't resovle the error i posted above when attempting to solve the equation.

thanks alot for your help, that has helped us progress although when we try to solve this i get the following error "Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {piecewise(R < a, -0.6670000000e14*R^3/max(H^4, (R-a)^4), a < R, 0.6670000000e14*a^4/(R*max(H^4, (R-a)^4)))}
"

this seems to suggest it isn't handling the piecewise function correctly.  I guess this is due to the fact that without values for R or a. With us solving for R the value for R should change as the equation is solved, and we do not have a value for a, although if i define a value for a with the other definitions then unapply claims they must be of the same type. Do you have any ideas as to getting piecewise to resolve in a way that will enable Maple to solve the equation?

If it helps here is the code for the boundary condiitons and the code used to solve the equation,

IBC := {S(0, t) = 0, S(99, t) = 0, S(R, 0) = f(R)};

pds1 := pdsolve(PDE1, IBC, numeric, S(R, t), time = t, range = 0 .. 99, spacestep = 0.1e-1, timestep = 0.25e-4);

Thanks very much for your help.