DOI: https://doi.org/10.24028/gzh.0203-3100.v37i6.2015.111180

### The study of convergence of additive-averaged splitting based on the scheme of explicit solution for three-dimensional equations of convective diffusion

L. Katsalova

#### Abstract

Modern mathematical forecast models are based on hydrodynamic equations, which are three-dimensional convection diffusion equations in the general form. In the article, the new approach to solving such equations, which consists in using the additive-averaged splitting on the basis of the explicit account method has been considered. The results of studies of stability and convergence of the method have been presented. Appropriate math grounds and evaluations have been given. Based on the results, conclusions regarding the effectiveness of the method for solving hydrodynamic equations are made.

#### Keywords

convection diffusion equation; additive-averaged splitting; explicit account method; stability; convergence

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