Exponential finite-difference schemes with double integral transformation for desicion of diffusion-convection equations

Object of this research are differential equations of diffusion-convection type. These equations are used for the description of many nonlinear processes in solids, liquids and gases. Despite a set of works on problems of their decision, they still present certain difficulties for the theoretical and numerical analysis. In the work the grid approach on the basis of the finite differences method for the solution of the equations of this kind is considered. For simplification of consideration the one-dimensional version of the equation was chosen. However the main properties of the equation are equal non-monotonicity and non-linearity were kept. For the solution of boundary problems for such equations the special variant of non-monotonic sweep procedure is offered.