Abstract
Explicit finite-difference schemes for the linear advection equations are considered. The schemes may be used in the advective step of the splitting method for the kinetic equations. The time derivative is approximated with first order by special asymmetric approximation. Schemes from first to fourth orders of approximation on space are constructed. Stability analysis is realized by von Neumann method. Stability criteria in the form of inequalities on Courant parameter are obtained. As it is demonstrated, obtained schemes demonstrate better stability properties in cases of high order asymmetric approximations in comparison with well-known explicit schemes.
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