Question: maple won't carry on calculation

I really need to be able to continue this calculation past nmax=14 but maple just won't do it.
I'd like to take it as far as possible. Does anyone know why maple won't calculate past nmax=14 and
if it can be overcome? Is this too difficult to achieve? I'm completely lost. can anybody help?

> with(LinearAlgebra);
> nmax:=14:
> Order:=nmax+1:

Start with the Navier-Stokes Equations rewritten as a differential equation (de1)
> de1:=diff(F(eta,R),eta$4)-R*(diff(F(eta,R),eta)*diff(F(eta,R),eta$2)-F(eta,R)*diff(F(eta,R),eta$3));

Write F in a series of powers of R
> S1:=series(eval(de1,F(eta,R)=add(F[k](eta)*R^k,k=0..nmax)),R):

Extract the individual equations for each power upto R^nmax
> des1:=[seq(coeff(S1,R,k),k=0..nmax)]:

Define the boundary conditions
> bcs:=k->(F[k](-1)=`if`(k=0,-1,0),F[k](1)=`if`(k=0,1,0),D(F[k])(-1)=0,D(F[k])(1)=0);

Solve the boundary value problem for each power
> for k from 1 to nmax+1 do
>     F[k-1]:=unapply(rhs(dsolve({des1[k],bcs(k-1)})),eta);
> end do;


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