Flow Exponential Schemes for Solving Equation of Convection-Diffusion Type

The object of the study is difference schemes for solving spatially one-dimensional equations of the convection-diffusion type. These equations are used to describe many nonlinear processes in solids, liquids and gases. A new finite-difference approach to solving equations of this type is proposed in the paper. To simplify the consideration, a spatially one-dimensional version of the convection-diffusion equation is chosen. However, the main features of the equation are preserved-non-monotonicity and quasi-linearity. Flow schemes with double exponential transformation and algorithms for their implementation are proposed to solving boundary and initial-boundary value tasks for the convection-diffusion equation.