Algorithm of the "$\alpha-\beta$ " iterations in the tasks simulation of the ionospheric plasma

The finite difference methods of the approximate solution of the multidimensional diffusion equations with mixed derivatives and first derivatives of a divergent type (convectional members) were examined. The problem leads to the chain of three twodimensional equations of a parabolic type on the basis of the method of a summary approximation. The finite difference operators were built and the analysis of their properties, test calculations and the estimation of the role of mixed derivatives were made. For finite differences elliptic equations solutions the modification of "$\alpha-\beta$ " iterational algorithm in case of diagonal predomination by columns is presented.