Till 2009 mathematical modelling in geodesy, astronomy and geophysics has been a major scientific field of the Department. The creator of this field and organizer and the head of the Department was prof. H. Meshcheriakov.
In 1987 Prof. H. Meshcheriakov and Associate Professor A. Tserklevych published a monograph “The gravitational field of Mars and areoid” and in 1994 a monograph by H. Meshcheriakov, V. Zinher, P. Zazuliak, M. Aheieva “Areoids and gravitational fields of Mars satellites”. One of the best research papers of the Theory of Mathematical Processing of Geodetic Measurements Department is O. Marchenko’s thesis “The external gravitational field modeling of the Earth based on the theory of potential non-central multipoles” for which he was awarded Physics Mathematics Ph.D. This paper presents the basis of the theory of potential non-central multipoles to describe the external gravitational field of the Earth, there is suggested a convenient mathematical device which, on the one hand, provides a formalization of the approximation of geopotential tasks solving both globally and locally, and on the other hand — it summarizes a number of researches on description of the gravitational field of the planet using multipoles and systems of point masses potentials.
Nowadays the researches on scientific field of mathematical modelling in geodesy, astronomy and geophysics are proceeded by Associate Professor M. Fys, who in 1986 defended thesis “Method of the density distribution constructing and the acceleration of gravity in the middle of terrestrial ellipsoid” and successfully works at the issue of the study of the planets internal structure by mathematical modelling of internal processes inside the planets, namely
- Construction of the three-dimensional models of density distribution and their coordination with the gravitational field parameters;
- Discovering internal potential and comparison of the external one with those calculated by the models;
- Research on the convergence of the gravitational field on the surface of the planet;
- Determination of gravitational energy of ellipsoidal planets and research on this basis the state of hydrostatic planets equilibrium.
Professor of the Department P. Zazuliak conducts research figure and gravitational field of the moon. Associate Professor A. Sohor studies the parameters of the reference-ellipsoid concordance of the Earth to the data on its regional gravity field.
In 2008 Lecturer A. Brydun defended his thesis on “The Fourier series method for meromorphic functions in half-strip” and applied research results to the function of Riemann.
At the Cartography and Geospatial Modelling Department were established scientific researches on the development of territories forecasting and their mapping taking into account the functional properties and effects of geodynamic processes headed by Prof., Ph.D. P. Cherniaha. Such studies are carried out on the basis of the mathematical modelling under conditions of uncertainty and systematic approach to mapping and GIS modelling. Ph.D. students and lecturers develop scientific approaches to mapping taking into consideration the spatial and temporal changes in the environment and socio-economic problems.