Abstract. The mathematical modeling of the propagation of contamination from point sources in the air is considered. An approach that uses the idea of splitting and point-to-point computing is proposed for the numerical solution of multi-dimensional convection-diffusion equations. The problems of the construction of splitting schemes, approximation, and stability on the initial data are investigated. Refs: 16 titles.

Keywords: convection–diffusion equation, splitting methods, numerical method, difference scheme, stability.