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 A Block-by-block method for the Impulsive Fractional Ordinary Differential Equations Junying Cao,Lizhen Chen,Ziqiang Wang Keywords:Impulsive fractional ordinary differential equations, block-by-block method, stability analysis, convergence analysis Abstract: In this paper, a block-by-block numerical method is constructed for the impulsive fractional ordinary differential equations (IFODEs). Firstly, the stability and convergence analysis of the scheme are established. Secondly, the numerical solution which converges to the exact solution with order $3+\gamma$ for $0<\gamma<1$ is proved, where $\gamma$ is the order of the fractional derivative. Finally, a series of numerical examples are carried out to verify the correctness of the theoretical analysis.