Additive schemes (splitting schemes) for systems of partial derivative equations

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.