A new algorithm has been developed that permits the direct time integration of Maxwell's equations in 2-D for material media having linear and nonlinear instantaneous and Lorentz-dispersive effects in the electric polarization. The optical carrier is retained in this approach. The fundamental innovation is the treatment of the linear and nonlinear convolution integrals which describe the dispersion as new dependent variables. By differentiating these convolutions in the time domain, an equivalent system of coupled, nonlinear, second-order ordinary differential equations is derived. These equations together with Maxwell's equations form the system that is solved to determine the electromagnetic fields in nonlinear dispersive media. The nonlinear modeling takes into account such quantum effects as the Kerr and Raman interactions. The new approach is robust and permits modeling optical soliton propagation, scattering, and switching directly from the full-vector, nonlinear Maxwell's equations for integrated optical structures.