The book discusses the main problems of approximate solution of convection-diffusion problems by numerical methods. Discrete models are derived from finite-difference and finite-element approximations. Monotonous difference schemes are constructed for problems with divergent and non-divergent convective transfer. Iterative methods are used to approximate the solution of net non-self-adjoint elliptic problems. On the basis of the general theory of stability (correctness) of operator-difference schemes, non-stationary problems of convection-diffusion . are investigated. The possibilities of applying additive difference schemes with splitting by spatial variables. are also discussed. The book is designed for specialists in computational methods of mathematical physics, mathematical modeling in the mechanics of continuous environments. The material is available to senior students of technical universities .