Geodesic
Additive schemes (splitting schemes) for systems of partial derivative equations
Numerical methods and programming, Tome 11 (2010) no. 1, pp. 1-6

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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. 
@article{VMP_2010_11_1_a0,
     author = {P. N. Vabishchevich},
     title = {Additive schemes (splitting schemes) for systems of partial derivative equations},
     journal = {Numerical methods and programming},
     pages = {1--6},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2010_11_1_a0/}
}
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P. N. Vabishchevich. Additive schemes (splitting schemes) for systems of partial derivative equations. Numerical methods and programming, Tome 11 (2010) no. 1, pp. 1-6. http://geodesic.mathdoc.fr/item/VMP_2010_11_1_a0/