No abstract

The conducted researches served as the basis for obtaining difference scheme for numerical realization of the two-dimensional model of mass transfer of a pollutant in the aeration zone of the soil of the agrolandscape with a piecewise smooth surface under the condition of instantaneous deposition of the pollutant onto the surface (as an example, Cs137 was taken as a pollutant on the basis of its passive behavior in the ground and the availability in the considered ground areas of agricultural uses due to the Chernobyl accident). The properties of differential operators of the model and their difference analogues were studied, which allowed to substantiate the cost-effective difference scheme for the numerical solution of the problem of pollutant migration for given agrolandscape. The correctness and efficiency of the constructed two-layer implicit difference scheme is shown. This allowed to switch to the use of a chain of one-dimensional implicit tasks, in which the transition from one layer to another occurs in two steps. Obtained general computing costs allowed to assert that the proposed schemes are cost-effective difference schemes. In turn, the use of an economical difference scheme made it possible to construct a method for the practical determination of the presence of a process of water erosion in the system of hydraulic rampart-terrace.

No abstract

No abstract

An analogue of the Galyorkin method for finding appro2rimate solutions to pseudoparabolic equations is proposed and the convergence of these approzimations to the generalized solution belonging to the class L2(Q) is demonstrated. Bibliography: 6 titles. This paper is devoted to the construction of art analogue of the Galyorkin method for finding approximate solutions to equations of the formwhere L = L(x) is a uniformly elliptic operator of the second order and M = M(a~) is a positive differential operator of the second kind, both defined in a finite dnm~i~ f~ C tl n with piecewise smooth boundary 0f~: m