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A new modified form of the rapid numerical difference recurrence formula was proposed to calculate the nonlinear Shrdinger equation,with ites of the pulse self-steepening and the intrapulse Raman scattering.Compared with the traditional analytical results of solitons and the solutions of Split-step Fourier method,the results show that the modified rapid numerical difference recurrence algorithm is a fast and precise numerical method,which takes into account simultaneously both the effects of the chromatic dispersion and the nonlinear Kerr effect together along each fiber segment,and the effects of all the higher-order nonlinear items of the optical medium.By using this method,it was validated successfully to simulate the supercontinuum generated as a result of the optical fiber nonlinear effects and the group velocity dispersion effects together.The formula was proved that it can provide some new ideas of research for the simulation of the other nonlinear phenomena in the optical medium.