A method for numerical solution of a multidimensional convection-diffusion problem (Q1040353)

Proposed paper presents numerical method for solving multidimensional convection-diffusion problems. Such type of problems arising for example from models of environmental processes in the Earth atmosphere, where to obtain significant results is often a difficult task. Presented method is based on the additive splitting algorithm using an efficient finite difference scheme and is a modification of the additive-averaged component wise splitting algorithm of \textit{D. G. Gordeziani} and \textit{G. V. Meladze} [Zh. Vychisl. Mat. Mat. Fiz. 14, 246--250 (1974; Zbl 0278.35049)]. The method allows parallel computations and presented modification reduces the number of data exchanges and their amount during the solution, which is the main improvement of presented method. Approximation, stability and conditional convergence of the type \(\tau=O(h^{1+s}), \;s \in (0,1) \) is investigated.