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A class of hybrid algorithms of real-time simulation based on evaluation of non-integerstep right-hand side function are presented in this paper. And some results of the convergence and stability of the algorithms are given. Using the class of algorithms, evaluation for the right-hand side function is needed once in every integration-step. Moreover, comparing with the other methods with the same amount of work, their numerical stability regions are larger and the method errors are smaller, and the numerical experiments show that the algorithms are very effective.