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Numerical modeling of system dynamics

ОК.10

Обов’язкова дисципліна для ОП

Second

2023/2024

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 purpose of the discipline "Numerical modeling of system dynamics" is to familiarize with the problems of numerical modeling of physical processes, in particular, hydrodynamics, to study general numerical modeling approaches that arise in hydrodynamics problems, and to learn techniques for constructing difference algorithms with the necessary properties. This discipline is a component of the educational and professional program of training specialists at the second (master's) level of higher education It is taught in the 2nd semester in the amount of 120 hours. (4 ECTS credits) in particular: lectures – 20 hours, laboratory hours – 18 hours. consultations 2 hours, independent work - 80 hours) The course includes 2 content modules and 3 laboratory works, an essay. The discipline ends with an exam. Course structure. The subject of the educational discipline "Numerical modeling of system dynamics" includes issues of linear and Hilbert spaces, Sobolev spaces, the main types of mathematical physics problems, generalized problem statements, correctness of mathematical methods, calculation schemes, practical use of developed system tools for solving numerical modeling problems applied mathematics and mathematical physics.

1. Rouch P. Vychislitelnaya gidrodinamika. M. “Mir” 1980. - 616 s. 2. Anderson D., Tannenhill Dzh., Pletcher R. Vychislitelnaya gidrodinamika i teploobmen. t 1, t 2, M. “Mir”, 1990 3. Samarskij A.A. Teoriya raznostnyh shem. M.:”Nauka” –1983 – 616s. 4. Grishenko O.Yu., Lyashko S.I. Metodi Fur’ye ta pershogo diferencialnogo nablizhennya v teoriyi riznicevih shem. – VPC ”Kiyivskij universitet”, 2005 – 84 s. 5. O.Yu. Grishenko, V.I.Lyashko, Onockij V.V. Dvokrokovi riznicevi algoritmi dlya giperbolichnih rivnyan pershogo poryadku z kerovanoyu shtuchnoyu v'yazkistyu. // Zhurnal obchislyuvalnoyi ta prikladnoyi matematiki. -2001. - №1(86). S. 20-28. 6. Rihtmajer R., Morton K. Raznostnye metody resheniya kraevyh zadach. – M.: “Mir” 1972 – 418 s. 7. Kollatc L. Funkcionalnyj analiz i vychislitelnaya matematika. –“Mir” ..

Lectures, laboratory workshop, independent work

Forms of student assessment: - 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