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Modern methods of computer modeling

ДВС.1.02

Вибіркова дисципліна для ОП

First

2022/2023

6 Semester

5

LO 6 Master the basic methods of developing discrete and continuous mathematical models of objects and processes, analytical research of these models for the existence and uniqueness of their solution. LO 18 Effectively communicate information, ideas, problems and solutions with specialists and society in general. PLO 22.1 Know the main sections of the theory of calculations, theory of algorithms and theory of programming, mathematical logic, theory of probability and mathematical statistics, control theory.

Full-time form

1. Know: Algebra, mathematical analysis, the theory of differential equations and numerical methods in the scope of the first two courses of the university. 2. Be able to: create programs in at least one programming language, use computer algebra systems, read and analyze mathematical texts, implement mathematical algorithms. 3. Possess elementary skills: working with a computer, searching for information on the Internet.

Module 1 General principles of computer modeling. Examples of problems, modern approaches, dimension problems, compromise between accuracy and speed, scaling. Models based on diff. equations with partial derivatives. Current state of development, advantages and disadvantages of different classes of algorithms: finite-difference approach, methods based on non-connections, finite-element approach. Systems of linear equations of large dimensions. Using the matrix structure to build effective methods. Algorithms for working with sparse matrices. Models for optimal control problems. Building a model based on applied problems. Optimal control of systems of differential equations with partial derivatives. Problems of impulse control. Current state of development of iterative algorithms for optimal control problems. Gradient descent methods. Modern variants of gradient methods. Modeling constraints in optimization problems. Problems and approaches. Use of projective type algorithms. Modern methods based on gradient projection. Extragradient methods. Examples of effective use of computer simulation. Consultation 2 Module 2 General characteristics of clustering methods. Basic approaches to the development of algorithms of this class ..

1. Liashko S.І., Sandrakov G.V., Semenov V.V., Kliushin D.A. Matematichne modeliuvannia ta obchisliuval-na matematika. Kiїv, VPТs “Kiїvs-kii unіversitet”, 2020 2. Makarov V.L., Gavriliuk I.P. Metodi obchislen-. Kiїv, Vishcha shkola, 1995 3. Samarskii A.A. Teoriia raznostnykh skhem. M., Nauka, 1989 4. Liashko S.І., Semenov V.V., Kliushin D.A. Spetsіal-nі pitannia optimіzatsії. Kiїv, VPТs “Kiїvs-kii unіversitet”, 2015 5. Lyashko S. I. Generalized optimal control of linear systems with distributed parameters. Boston / Dordrecht / London: Kluwer Academic Publishers, 2002 6. Vasil-ev F.P. Metody resheniia ekstremal-nykh zadach. M.: Nauka, 1981 7. Panteleev, D.V. Metlitskaia, E.A. Aleshina Metody global-noi optimizatsii. Metaevristicheskie strategii i algoritmy A. V. 2013,. M. Vuzovskaia nauka

Lectures, practical, independent work

- semester assessment: 1. Project-1: RN1.2, RN2.1, RN2.2, RN2.3, RN3.1, RN4.1, RN4.2 – 15 points / 9 points 2. Project-2: RN1.3, RN2.1, RN2.2, RN2.3, RN3.1, RN4.1, RN4.2 – 15 points / 9 points 3. Project-3: PH1.4, PH2.1, PH2.2, PH2.3, PH3.1, PH4.1, PH4.2 - 15 points / 9 points 4. Project-4: RN1.5, RN2.1, RN2.2, RN2.3, RN3.1, RN4.1, RN4.2 – 15 points / 9 points final assessment is conducted in the form of an exam. the maximum number of points that can be obtained by a student: 40 points; - learning outcomes that will be assessed: PH1.1 - PH1.6, PH2.1, PH3.1; - form of implementation and types of tasks: written ..

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