Nataliya A. Computation Algorithms and Automation of Calculations for Nonstationary Processes in Multicomponent Environments.

The thesis proposes new mathematical models of nonstationary diffusion processes running in multicomponent soil environments, that contain arbitrarily oriented in space thin inclusions or cracks. The proposed models are formulated as new classes of initial boundary-value problems for parabolic-type equations with heterogeneous conjugation conditions. To find approximated generalized discontinuous solutions to the considered problems, computation algorithms with a higher accuracy order are created. Estimates are obtained for errors of approximate generalized solutions, made by the finite-element method, and also estimates for errors of approximate solutions derived by the difference Krank-Nicholson scheme and discontinuous functions. The computer-aided NADRA system is built on the basis of the developed computation algorithms. Such system is aimed at investigation of the above-mentioned processes. Computational experiments are carried out. A problem is solved that has found its practical application. Keywords: mathematical modelling, nonstationary filtration, initial boundary-value problem, multicomponent environment, thin inclusion, highly-accurate algorithms, computer-aided system.