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Analytical expressions involving both system parameters and step-size are proposed to represent the local simulation error for the symmetrized split-step Fourier (SSSF) simulation method. This analytical expression can be used for a step-size selection rule to achieve comparable local simulation accuracy for SSSF simulations. This can lead to computational savings since there is no waste of computation in each simulation step. Furthermore, based on the local error expression, scaling rules are derived to achieve comparable global simulation accuracy for wide ranges of key system parameter values. This is significant in enhancing the computational efficiency in optical fiber communication system design and optimization. Extensive validation tests were performed to explore the application range of the proposed step-size selection and scaling rules. The desired global accuracy can be achieved with the use of our local error expression and scaling rules by only a couple of test trial simulation runs for a variety of practical applications.