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An efficient algorithm, which exhibits a fourth-order global accuracy, for the numerical solution of the normal and generalized nonlinear Schrodinger equations is presented. It has applications for studies of nonlinear pulse propagation and spectral broadening in optical fibers. Simulation of supercontinuum generation processes, in particular, places high demands on numerical accuracy, which makes efficient high-order schemes attractive. The algorithm that is presented here is an adaptation for use in the nonlinear optics field of the fourth-order Runge-Kutta in the Interaction Picture (RK4IP) method, which was originally developed for studies on Bose-Einstein condensates. The performance of the RK4IP method is validated and compared to a number of conventional methods by modeling both the propagation of a second-order soliton and the generation of supercontinuum radiation. It exhibits the expected global fourth-order accuracy for both problems studied and is the most accurate and efficient of the methods tested.