Parameter optimization algorithms of difference calculation schemes for improving the solution accuracy of diffusion equations describing the pollutants transport in rivers

The problems related to practical realization (as a computer program) of difference schemes of the solution of diffusion equations that describe pollutants transport in the river water are considered in this paper. In particular, the problems of optimum choosing of the algorithm parameters on which depend the accuracy, the time and the possibility of practical realization of the equation solution are considered. The demand to reduce as much as possible the time and the errors of calculations, and also the simplicity of the functions of certain classes used in mathematical models and their maximum accordance to real physical conditions are considered as criteria of optimality.