О развитии приближенных методов исследования процессов в блочно структурированной среде

Abstract

We need to consider the model of the medium as close as possible to the natural one, to apply a mathematical apparatus that adequately and reliably describes the processes and phenomena occurring in the studied medium of a complex structure in the process of creating modern systems for monitoring the geophysical medium, regulating the quality of the environment. Such a possibility is provided by methods having a topological basis, in particular, a differential factorization method. However, with strict adherence to the algorithm, the numerical evaluation of the parameters under study requires considerable time. Therefore, it is necessary to identify those moments where it is possible to proceed to an approximate solution without compromising the accuracy of the result obtained. A method is proposed for constructing approximate solutions of systems of integral equations arising in the investigation of boundary problems of the mechanics of a solid deformed body and the mechanics of continuous media by a differential factorization method for media of complex structure. The justification of the proposed conclusions for the problems posed both in Cartesian and curvilinear coordinate systems is fulfilled. As an example, the application of approximate methods in problems of assessing the quality of the aquatic environment or the atmosphere is considered. The results can be used for express forecast of the ecological state of the environment, in systems of integrated geoecological monitoring.