Exponential finite-difference schemes with double integral transformation for the solution of diffusion-convection equations (Q2925053)

The application of diffusion-convection equations for the analytical and numerical investigation of many nonlinear processes in rigid bodies, liquids and gases mets some difficulties. Here, the net approach on the base of the finite difference method is used for the solutions of the above mentioned types of equations. To simplify the analysis, a spatial one-dimensional variant of the equation was chosen but the base singularities of the equations, i.e., non-monotonicity and non-linearity were kept. A special variant of the non-monotonous sweep method is suggested for the solution of boundary problems of the discussed equations.