Infopaket

Theory of difference methods

ДВС.1.05

Вибіркова дисципліна для ОП

First

2023/2024

7 Semester

4

LO 9. Build efficient algorithms regarding the accuracy of calculations, stability, speed and cost of system resources for numerical study of mathematical models and solution of practical problems. LO 15. Be able to organize their own activities and get results within limited time. PLO25.1 Be able to use computer systems to implement computational algorithms and mathematical modeling.

Full-time form

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 is to get acquainted with the problems of applying difference schemes in numerical modeling of physical processes, to study general approaches of numerical modeling and to master the methods of constructing difference algorithms with the necessary properties. This discipline is a component of the educational and professional program of training specialists at the first (bachelor's) level of higher education It is taught in the 7th semester in the amount of 120 hours. (4 ECTS credits) in particular: lectures – 42 hours, consultations 6 hours) The course includes 3 content modules and 2 modular control papers, an essay and essay defense. The discipline ends with a final assessment. The goal and task of the educational discipline "Theory of difference methods" is to familiarize with the problems of numerical modeling of physical processes, in particular, hydrodynamics, to study the general approaches of numerical modeling that arise in problems of hydrodynamics, and to master the techniques of constructing difference algorithms with the necessary properties. Course structure. The subject of the educational discipline "Theory of Difference Methods" 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 problems of numerical modeling of applied of mathematics and mathematical physics.

1. Rouch P. Vyichislitelnaya gidrodinamika. M. “Mir” 1980. – 616s. 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. – 616s. 4. Hryshchenko O.Iu., Liashko S.I. Metody Furie ta pershoho dyferentsialnoho nablyzhennia v teorii riznytsevykh skhem. – VPTs ”Kyivskyi universytet”, 2005. – 84 s. 5. Rihtmayer R., Morton K. Raznostnyie metodyi resheniya kraevyih zadach. –M.: “Mir” 1972. – 418 s. 6. 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. 7. Kollatts L. Funktsionalnyiy analiz i vyichislitelnaya matematika. –“Mir” 8. Godunov S.K., Ryabenkiy V.S. Raznostnyie shemyi.– M.:”Nauka” –1977. – 440s. ..

Lectures, independent work.

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

Ukrainian