Difference approximations in time are considered in the case of approximate solving the Cauchy problem for a special system of first-order evolutionary equations. Unconditionally stable two-level operator-difference schemes with weights are constructed. A second class of difference schemes is based on a formal transition to explicit operator-difference schemes for a second-order evolutionary equation at explicit--implicit approximations of specific equations of the system. The regularization of such schemes for obtaining unconditionally stable operator-difference schemes are discussed. Splitting schemes associated with solving some elementary problems at every time step are proposed.

Keywords: Cauchy problem, systems of evolutionary equations, operator-difference schemes, stability

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