Quantized State System (QSS) is a new numerical integration method based on discretization of state variables. Different from traditional time discretization methods, QSS advances the next integration by calculating the time required for each transition of the state variables. Despite its advantages over traditional methods in solving non-stiff ordinary differential equations, it is not suitable for solving stiff problems. Therefore, an adaptive multi-step correction algorithm based on QSS (AMCQSS) is proposed, combining the ideas of the QSS method and the implicit multi-step method. The AMCQSS can adaptively choose two-step or three-step methods in the calculation process to effectively improve the accuracy and efficiency of solving stiff problems. The feasibility of this algorithm is verified by the simulation of flexible spacecraft dynamics. The comparison of performance between this algorithm and the previous methods of ODE23tb, ODE15s, ODE45 and QSS shows that the AMCQSS can ensure the solution efficiency and accuracy with good convergence and stability.
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