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Numerical modeling of system dynamics.

Обов’язкова дисципліна для ОП

Second

2021/2022

2 Semester

4

PLO2. Understanding of the principles and methods of analysis and evaluation of the range of tasks that contribute to the further development of effective use of information resources.

Students must know the relevant sections of the methods of approximate calculations, namely finite-difference methods for solving boundary value problems, methods of linear algebra, approximation of operators; methods of functional analysis; differential equations; Fourier series theory and other mathematical methods.

The aim of the discipline is to get acquainted with the problems of numerical modeling of physical processes, including hydrodynamics, study general approaches to numerical modeling that arise in hydrodynamics, and learn techniques for constructing difference algorithms with necessary properties. It is taught in the amount of 120 hours. In particular: lectures - 20 h, laboratory - 18 h. consultations 2 h, independent work - 80 h.) The course includes 2 content modules and 3 laboratory works, abstract. The discipline ends with an exam. Course structure. The subject includes questions of linear and Hilbert spaces, Sobolev spaces, basic types of mathematical physics problems, generalized problem statements, correctness of mathematical methods, computational schemes, practical use of developed system tools for solving numerical modeling problems.

1. Rouch P. Vyichislitelnaya gidrodinamika. M. “Mir” 1980 2. Anderson D., Tannenhill Dzh., Pletcher R. Vyichislitelnaya gidrodinamika i teploobmen. t 1, t 2, M. “Mir”, 1990 3. Samarskiy A.A. Teoriya raznostnyih shem. M.:”Nauka” –1983 4. Hryshchenko O.Iu., Liashko S.I. Metody Furie ta pershoho dyferentsialnoho nablyzhennia v teorii riznytsevykh skhem. – VPTs ”Kyivskyi universytet”, 2005. – 84 s. 5. O.Iu. Hryshchenko, V.I.Liashko, Onotskyi V.V. Dvokrokovi riznytsevi alhorytmy dlia hiperbolichnykh rivnian pershoho poriadku z kerovanoiu shtuchnoiu viazkistiu. // Zhurnal obchysliuvalnoi ta prykladnoi matematyky. -2001. - №1(86). S. 20-28. 6. Rihtmayer R., Morton K. Raznostnyie metodyi resheniya kraevyih zadach. –M.: “Mir” 1972 7. Kollatts L. Funktsionalnyiy analiz i vyichislitelnaya matematika. –“Mir” ..

Lectures, laboratory workshop, independent work.

- semester assessment: 1. Laboratory work 1: 15 points / 9 points. 2. Laboratory work 2: 15 points / 9 points. 3. Laboratory work 3: 15 points / 9 points. 4. Summary: 15 points / 9 points. A student is admitted to the exam if he scored more than 36 points during the semester. To obtain an overall positive grade in the discipline, the grade for the exam can not be less than 24 points.

Ukrainian