A new approach is developed for fast solution of complex dynamic problems in nonlinear optics. The model is based on the nonlinear Maxwell’s equations coupled with time-dependent electron density equation. The approach is based on the Finite-Difference Time-Domain (FDTD) and the auxiliary differential equation (ADE) methods for frequency-dependent Drude media with a time-dependent carrier density, changing due to Kerr, photoionization, avalanche and recombination effects. The system of nonlinear Maxwell-Ampere equations is solved by an iterative fixed-point procedure. The proposed approach is shown to remain stable even for complex nonlinear media and strong gradient fields. Graphics-processing-units (GPU) technique is implemented by using an efficient algorithm enabling solution of massively three-dimensional problems within reasonable computation time.