# Department of Computational Mathematics

**General description**

The Department of Computational Mathematics is a structural unit of the Institute of Computation Mathematics and Information Technologies of Kazan (Volga Region) Federal University. Jointly with other Institute units the Department provides teaching for students according to the bachelor and master programs in the directions of studying: “Applied Mathematics” and “Applied Mathematics and Informatics”. The Department specializes students in the field of numerical methods and mathematical modeling. The Department has post-graduate programs in the directions of studying: 01.01.07 – computational mathematics, 05.13.18 – mathematical modeling, numerical methods and program complexes. Also the Department gives mathematical and information technologies lessons in other University units. Currently the Department has seventeen teaching staff members, among them there are nine doctors and four candidates of physical and mathematical sciences among them.

**History**

Department of Computational Mathematics was organized in 1975 under the initiative of Professor A.D. Lyashko (1930–2008) on the base of research seminar which was led by him since 1965. The seminar was specialized in the field of numerical methods for solving nonlinear problems of mathematical physics. Initially, the seminar united researchers of Mechanics and Mathematics Faculty of Kazan State University. After founding the Computational Mathematics and Cybernetics Faculty in 1978 the Department became a structural unit of the Faculty. The research seminar continued to work on the new Faculty engaging in the research most active students. These students after graduation joined the Department. By the end of the seventies the Department became one of the leading scientific centers of the country in the field of numerical methods for solving mathematical physics nonlinear problems. Professor A.D. Lyashko headed the Department until 1998.

From 1998 to 2013 the Department was headed by Professor M.M. Karchevskiy. According to the fast development of computer and information technologies in this period the research topics is also expanded and updated, including current issues of theoretical and applied directions of mathematical modeling and computational mathematics. From 2013 to 2019 the Department is headed by Professor O.A. Zadvornov. This period is characterized by structural changes at the university and foundation of the Institute of Computation Mathematics and Information Technologies. By now in the Kazan University a scientific school has been established, which is one of the main centers of research in the field of numerical methods for solving problems of mathematical physics and mathematical modeling.

**The information about the Department head**

Since 2019 the Department is headed by Professor R.Z. Dautov. Rafail Zamilovich Dautov is a Doctor of Physical and Mathematical Sciences and a Professor of the Department of Computational Mathematics. Professor R.Z. Dautov is widely known both in Russia and abroad as a major specialist in the field of numerical methods and mathematical modeling of continuum mechanics problems. He also has a rich and successful experience in solving applied problems in oil production, computation of thin-walled structures, thermal physics, electrophysical methods of flaw detection, etc. He is the author of the well-known books in the field of numerical methods for solving problems of mathematical physics. R.Z. Dautov has a rich experience in teaching at the Institute. He developed a large number of general and special courses, series of tasks widely used by teachers of the Institute for laboratory and practical work. Several candidate and doctoral dissertations in the fields of computational mathematics and mathematical modeling were defended under his supervision and with his active help

**Educational activities**

Teachers of the Department are teaching students of the Institute on general disciplines: numerical methods, mathematical physics equations, information technology, computer architecture, the concept of modern science. For Computational Mathematics Department students teachers give lectures and seminars on special disciplines: applied functional analysis, additional chapters of mathematical physics equations, finite difference methods for solving problems of mathematical physics, finite element method. Teachers of the Department supervise the implementation of the course and final qualifying works of bachelors and masters, lead the research work of post-graduate students.

**Scientific research**

The Department Staff members have obtained the following results:

the method of summation identities for nonlinear problems of physics, mechanics, biology has been proposed and investigated (A.D. Lyashko, M.M. Karchevskiy, V.D. Glushenkov);

the correctness theory of nonlinear operator-difference schemes has been developed, new efficient finite difference schemes for nonlinear non-stationary equations of mathematical physics have been constructed (A.D. Lyashko, A.V. Lapin, M.M. Karchevskiy, E.M. Fedotov);

new versions of the finite element method for elliptic equations, variational inequalities and eigenvalue problems have been constructed and investigated (M.M. Karchevskiy, R.Z. Dautov, S.I. Solov'ev);

the theory of finite-dimensional approximations for nonlinear eigenvalue problems has been developed, numerical methods for solving nonlinear spectral problems arising in science and technology have been constructed and studied (A.D. Lyashko, R.Z. Dautov, S.I. Solov'ev);

mesh schemes for stationary and non-stationary degenerate equations, for equations with singularities of solutions, with applications to problems of filtration theory, joint motion of ground and surface waters have been studied (A.D. Lyashko, A.V. Lapin, Yu.B. Smirnov, M.M. Karchevskiy, R.Z. Dautov, M.R. Timerbaev, M.F. Pavlova, L.L. Glazyrina);

new mathematical models, mesh approximations and numerical realization methods for problems of nonlinear filtration theory, the theory of filtration consolidation, biomechanics of internal organs, nonlinear theory of plates and shells, soft shells theory have been proposed and investigated (A.D. Lyashko, M.M. Karchevskiy, A.V. Lapin, R.Z. Dautov, I.B. Badriev, O.A. Zadvornov, S.N. Voloshanovskaya, R.R. Shagidullin, M.F. Pavlova, R.N. Miftakhov, G.R. Abdyusheva, M.I. Drobotenko, M.E. Mayorova, E.V. Rung);

computational procedures and program complexes for the calculation of friction bearings of turbo-compressor machines for thermal fields of spiral compressors and vacuum pumps for the joint research project of Scientific Research Institute “Turbokompressor” in Kazan have been developed (M.M. Karchevskiy, R.Z. Dautov, E.M. Fedotov, N.N. Sarimov, V.D. Glushenkov, V.L. Gnedenkova).

The Department Staff members lead large scientific and organizational work. Among them there are members of Dissertation Councils of Kazan Federal University and Kazan Technology University, editorial board members of the journals: “Russian Mathematics (Iz. VUZ)”, “University Proceedings. Volga Region. Physical and Mathematical Sciences”, “Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki”. Ten Russian and international scientific conferences “Mesh methods for boundary value problems and applications” were organized on the base of the Department from 1996 to 2018.

**Graduates**

The best graduates of the Computational Mathematics Department continue research in post-graduate study, take the candidate and the doctoral degrees, join the Department, work in the Russian and foreign universities. Many graduates of the Department successfully work in IT-companies, banks, various private and state organizations of the country and abroad.

**Interesting facts**

Staff members of Computational Mathematics Department participated in international research projects:

“Simulation of two-dimensional gravity-driven unstable flow” (USA, R.Z. Dautov);

“Numerical simulation of motility patterns of the small bowel” (UK, G.R. Abdyusheva, R.N. Miftakhov);

“Stability analysis, low-dimensional modeling, and optimal control of the flow around a circular cylinder” (Germany, K.Е. Afanas'ev);

“Computation of corner singularities for linear elasticity” (Germany, S.I. Solov'ev);

“Preconditioned iterative methods for nonlinear eigenvalue problems” (Germany, S.I. Solov'ev).

**Links**

The department site: http://kvm.kpfu.ru