  We present an {\it ab initio} and non-perturbative time-dependent approach to
the problem of double ionization of a general atom driven by intense XUV laser
pulses. After using a highly flexible $B$-Spline $R$-matrix method to generate
field-free Hamiltonian and electric dipole matrices, the initial state is
propagated in time using an efficient Arnoldi-Lanczos scheme. Test calculations
for double ionization of He by a single laser pulse yield good agreement with
benchmark results obtained with other methods. The method is then applied to
two-color pump-probe processes, for which momentum and energy distributions of
the two outgoing electrons are presented.
