We present a moving adaptive grid method for solving the time-dependent Schrodinger equation, TDSE, for molecules in intense laser fields, applicable in the nonperturbative nonlinear regime where dissociation ionization occurs. The method is based on a Lagrangian, moving coordinate system. In this representation, the reference system is moving with the laser pulse so that the classical movement of free particles in the field, i.e., in the asymptotic region where electron-molecule potentials are negligible but the laser field is still present, is exactly described. As a consequence, the asymptotic quantum wave functions are exact in presence of a laser pulse. We have tested several discrete propagator methods for the TDSE in different gauges in a Born-Oppenheimer simulation of H-2(+) in a short, intense laser pulse. Our comparison of convergence between the same discretization methods for different gauges have demonstrated the superiority of the present Lagrangian adaptive grid method to treat the response of molecules to intense time-dependent electromagnetic fields.