Exponential difference schemes for solution of boundary problems for diffusion-convection equations

The numerical solution of boundary-value problems is considered for multidimensional equations of convection-diffusion (CDE). These equations are used for many physical processes in solids, liquids and gases. A new approach to the spatial approximation for such equations is proposed. This approach is based on a integral transformation of second order differential operators. A linear version of CDE was selected to simplify analysis. For this variant, a new exponential difference schemes were offered, algorithms of its implementation were developed, a brief analysis of the stability and convergence was fulfilled. Numerical testing of approach was executed for a two-dimensional problem of metallic particles motion in the water flow under influence of a constant magnetic field.