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Numerical simulation of pulse propagation in nonlinear optical fiber based on nonlinear Schrodinger equation plays a significant role in the design, analysis, and optimization of optical communication systems. Unconditionally stable operator-splitting techniques such as the split-step Fourier method or the split-step wavelet method have been successfully used for numerical simulation of uniformly time-sampled pulses along nonlinear optical fibers. Even though uniform time sampling is widely used in optical communication systems simulation, nonuniform time sampling is better or even desired for certain applications. For example, a sampling strategy that uses denser sampling points in regions where the signal changes rapidly and sparse sampling in regions where the signal change is gradual would result in a better replica of the signal. In this paper, we report a novel method that extends the standard operator-splitting techniques to handle nonuniformly sampled optical pulse profiles in the time domain. The proposed method relies on using cubic (or higher order) B-splines as a basis set for representing optical pulses in the time domain. We show that resulting operator matrices are banded and sparse due to the compact support of B-splines. Moreover, we use an algorithm based on Krylov subspace to exploit the sparsity of matrices for calculating matrix exponential operators. We present a comprehensive set of analytical and numerical simulation results to demonstrate the validity and accuracy of the proposed method.