Geodesic
SM-stability of operator-difference schemes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 6, pp. 1002-1009

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The spectral mimetic (SM) properties of operator-difference schemes for solving the Cauchy problem for first-order evolutionary equations concern the time evolution of individual harmonics of the solution. Keeping track of the spectral characteristics makes it possible to select more appropriate approximations with respect to time. Among two-level implicit schemes of improved accuracy based on Padй approximations, SM-stability holds for schemes based on polynomial approximations if the operator in an evolutionary equation is self-adjoint and for symmetric schemes if the operator is skew-symmetric. In this paper, additive schemes (also called splitting schemes) are constructed for evolutionary equations with general operators. These schemes are based on the extraction of the self-adjoint and skew-symmetric components of the corresponding operator. 
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     title = {SM-stability of operator-difference schemes},
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P. N. Vabishchevich. SM-stability of operator-difference schemes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 6, pp. 1002-1009. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_6_a5/