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A new method to solve the stochastic Liouville equation in the time domain has been developed. The effective and accurate algorithm designed conserve the norm of the propagator at every time step. The algorithm is not dependent on how the fluctuations are generated. The method is applied to solve the stochastic Liouville equation of an electron spin, S=1/2, coupled to a nuclear spin system with spin quantum number I=1. The calculated slow-motion electron spin resonance (ESR) line shapes presented are for a model where the stochastic time dependent spin-lattice coupling was obtained from a Brownian dynamic simulation of restricted reorientation in a cone potential. These spectra were then compared with the spectra obtained by solving the stochastic Liouville equation (SLE) using the eigenfunction expansion method. All spectra conform exactly and the computer power used by the two methods are similar.

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