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To meet rapidly increasing bandwidth requirements, extensive numerical simulations are an important optimization step for optical networks. Using a basis of cardinal functions with compact support, a new split-step wavelet collocation method (SSWCM) was developed as a general solver for the nonlinear Schrödinger equation describing pulse propagation in nonlinear optical fibers. With N as the number of discretization points, this technique has the optimum complexity O(N) for a fixed accuracy, which is superior to the complexity O(Nlog2N) of the standard split-step Fourier method (SSFM). For the simulation of a large 40-Gb/s dense-wavelength-division-multiplexing (DWDM) system with 64 channels, the SSWCM requires less than 40% of computation time compared with the SSFM. This improvement allows a systematic optimization of wavelength-division-multiplexing (WDM) system parameters to achieve a minimum bit-error rate.