Scientific and pedagogical schools founded by A. S. Kholodov

Abstract

In the science development an important role the scientific schools are played. This schools are the associations of researchers connected by the common problem, the ideas and the methods used for problems solution. Usually Scientific schools are formed around the leader and the uniting idea. The several sciences schools were created around academician A. S. Kholodov during his scientific and pedagogical activity. This review tries to present the main scientific directions in which the bright science collectives with the common frames of reference and approaches to researches were created. In the review this common base is marked out. First, this is development of the group of numerical methods for hyperbolic type systems of partial derivatives differential equations solution - grid and characteristic methods. Secondly, the description of different numerical methods in the undetermined coefficients spaces. This approach developed for all types of partial equations and for ordinary differential equations. On the basis of A. S. Kholodovs numerical approaches the research teams working in different subject domains are formed. The fields of interests are including mathematical modeling of the plasma dynamics, deformable solid body dynamics, some problems of biology, biophysics, medical physics and biomechanics. The new field of interest includes solving problem on graphs (such as processes of the electric power transportation, modeling of the traffic flows on a road network etc). There is the attempt in the present review analyzed the activity of scientific schools from the moment of their origin so far, to trace the connection of A. S. Kholodovs works with his colleagues and followers works. The complete overview of all the scientific schools created around A. S. Kholodov is impossible due to the huge amount and a variety of the scientific results. The attempt to connect scientific schools activity with the advent of scientific and educational school in Moscow Institute of Physics and Technology also becomes.

Keywords

• scientific school
• grid and characteristic methods
• undetermined coefficients spaces
• the plasma dynamics
• the deformable solid dynamics
• biomechanics
• processes on graphs