✍ Scribed by A.P. Mikhailov; V.G. Novikov
No coin nor oath required. For personal study only.
The programme was a follows. I. Theory of computational methods for problems of mathematical physics. 2. Mathematical modelling of typical problems of mathematics and physics. 3. Methods of analyzing the properties of matter. 4. Packages of programs for applied mathematics and physics. Papers of a review character on specific problems of computational mathematics were read by the participants and discussed at the seminars.
Academician Samarskii stressed in his introductory lecture that the rapid development of science imposes increased demands on scientists, particularly on those involved in computational mathematics. This is, above all, a question of the management of science, of correctly forecasting its development, and the choice of the most up-to-date trends. All the factors which influence one or another trend in science, and the education of young specialists who are able to use modern methods of research, must be taken into account.
Speaking of the specific problems of computational mathematics, Academician Samarskii pointed to the need for the further development of all trends of the 'computational experiment' and the application of these, both in the traditional and in the modern domain. In particul~r, the use of computational methods requires additional effort in developing analytical methods for solving non-linear problems of mathematical physics.
Apart from its main purpose, the computational experiment is a good tool for constructing satisfactory mathematical models which, having obtained recognition, will become an independent subject of research in the future.
The question of creating effective discrete models, their realization on a computer, and the development of the theory of computational methods, remains as important as before. The design of the hardware for computational experiments is important, together with a comparison of this experiment with the scientific one.
In this connection the need arises to develop a method of processing the results of full-scale experiments.
These problems are solved in the framework of special computational experiments accompanying the basic research.
Academician Samarskii remarked that the compilation of a package of programs for the applied sciences means that the computational research has been sufficiently developed, that is, the class of problems has been formulated, methods of solving them have been worked out, and reliable mathematical models and algorithms have been set up. He gave examples of various packages of programs available in the USSR, and gave a brief description of some new methods of constructing discrete models of various problems in physics and technology.
The basic trends in computational research were reflected in detail in the programme of lectures.
In accordance with the programme of the school, the following papers were read. i. V.L. Makarov, 'Coordinated a priori estimates in the theory of difference schemes'; V.B. Andreev, 'The method of finite elements'.
Examples of structures and mathematical models of some biological and ecological processes'; A.P. Mikhailov, 'The self-similar model in nonlinear problems of mathematical physicis'; and S.I. Pokhozhaev, 'On the growth of a non-linear operator relative to the subordinate terms'.
Special thematic days devoted to some modern problems, particularly the problems studied in the Latvian Scientific Research Institutes, were organized at the school.
--The numerical modelling of crystallization processes was the subject of the following lectures: I.V. Fryazinov, 'Conservative monotonic difference schemes for the Navier-Stokes equations'; N.A. Avdonin, 'The mathematical description and solution of some problems of crystallization'; and V.I. Polezhaev, '~thematical models of hydrodynamic processes and
📜 SIMILAR VOLUMES
Kinematical properties of gravitation which are equivalent to the geodetic hypothesis of Einstein's theory of gravitation are looked for. It is shown that a generalized vorticity theorem, as well as the possibility of synchronizing adjacent clocks during a finite time interval, characterize Einstein