Mathematical modeling has a special position in space research.
This is due to the following reasons:
– cosmic phenomena is extremely difficult to predict and therefore almost impossible to plan, that is impossible to put the experiment so as to separate one thing from another;
– monitoring of the space phenomena is carried out from Earth and from space. The precision of observations from Earth is limited by different properties of Earth’s atmosphere.
– direct measurement of space plasma parameters are possible only by satellite and so are local in nature;
– space experiments on orbital stations are very expensive and therefore require careful preparation on Earth.
The mentioned above features of space experiments require as well prior mathematical modeling to analyze and anticipate the possible course of physical processes i.e. solving of direct problems, as inverse solution – restore the whole picture of the physical process based on a mathematical model (formal or physical) of process and local measurements data.
– Development of mathematical models of physical processes in space and numerical and analytical methods for solving equations describing these processes and recovery methods of physical fields using the results of local measurements.
– Developed the numerical methods for calculating of acoustic gravity waves in the ionosphere.
– Developed the numerical methods for calculation of main modes of small perturbations of the magnetosphere.
– Developed based on the finite-element Petrov-Galerkin method algorithms and programs of direct and inverse problems of MHD.