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The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations. The sensitivity of the difference scheme to initial values is further analyzed. The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined. Thus, the computational stability is sensitive to the initial perturbations.