The work contains the approximation of the third boundary value problem of schemes of high order. The approximation of the operator of the convective and diffusive transport difference schem were obtained, which has the fourth-order approximation error. The discrete operator diffusive transport in the absence of the influence of the boundary was considered.The construction of schemes of higher order accuracy approximates the operator diffusive transport in the border nodes in the case of boundary conditions of the third kind with the second order of accuracy was found.

Keywords: Schemes of high order, diffusion, diffusion transfer, discrete operator, approximation, boundary conditions, boundary value problem, finite-difference scheme

The work contains the construction and software implementation of related software systems designed for mathematical modeling of processes occurring in coastal water systems. The space-two-dimensional model of sediment transport in shallow waters allows to forecast the dynamics of bottom topography changes by reason of the movement of water and solid particles, to take into account the porosity of the soil, the critical shear stress at which begins the movement of sediment, turbulent exchange, dynamically changing geometry of the bottom, wind currents and friction on the bottom. The mathematical model of motion of a multicomponent air, takes into account factors such as the transport of pollutants and heat; the effect of vegetation; change in the coefficient of turbulent exchange; water transfer from the liquid to the gaseous state and others.

Keywords: multiprocessor computer system, grid equations, suspended solids, sediment