Infopaket

Theory of difference schemes

Вибіркова дисципліна для ОП

First

2023/2024

7 Semester

1

LO 6. Have the basic methods of analytical research of mathematical models of objects and processes for the existence and uniqueness of their solution. LO 10. Build algorithms that are efficient in terms of calculation accuracy, stability, speed and cost of system resources for numerical study of mathematical models and solving practical problems. LO 12. Be able to apply modern technologies of programming and software development, software implementation of numerical and symbolic algorithms. LO 16. Be able to organize their own activities and get results within a limited time. LO 19. Communicate effectively on information, ideas, problems and solutions with professionals and society as a whole. PLO 21. Demonstrate professional communication skills, including oral and written communication in Ukrainian and at least one of the common European languages. PLO 26.1. Be able to use computer systems to implement computational algorithms and mathematical modeling.

Distance 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 and objectives of the discipline "Theory of difference schemes" 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. Course structure. The subject "Theory of difference schemes" includes questions of linear and Hilbert spaces, Sobolev spaces, basic types of problems of mathematical physics, generalized problem statements, correctness of mathematical methods, computational schemes, practical use of developed system tools to solve problems of numerical modeling. 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. 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. – 418 s. 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.

- 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 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