Infopaket

Numerical methods of mathematical physics

Обов’язкова дисципліна для ОП

First

2021/2022

7 Semester

4

LO 3. Formalize problem sets up in the language of a particular subject area; define their mathematical formulation and choose a rational problem-solving approach; solve the obtained problems with analytical and numerical methods, evaluate the accuracy and reliability of the results obtained. LO 5. Be able to develop and use in practice algorithms related to the approximation of functional dependencies, numerical differentiation and integration, solving systems of algebraic, differential and integral equations, solving boundary value problems, finding optimal solutions.

Full-time form

To successfully learn the discipline "Numerical methods of mathematical physics" the student should satisfy the following requirements: know: (a) the basic definitions and theorems of mathematical analysis, algebra, theory of differential equations, fundamentals of calculation methods, equations of mathematical physics; (b) procedural and object-oriented programming. be able: (a) to solve problems of mathematical analysis, algebra, the theory of differential equations by classical methods, fundamentals of calculation methods; (b) to program in procedural and object-oriented styles.

Block 1. Projection-variation methods for solving operator equations. Methods of moments, Bubnov-Galorkin, collocation, Ritz, least squares. Statement of the problem in generalized spaces. Convergence of methods. Methods of constructing basic functions. Examples of application of methods to boundary value problems. Block 2. Difference methods for solving boundary value problems. Methods of approximation of basic differential operators. Basic methods of constructing difference schemes. Approximation of boundary conditions. Schemes of the increased order of approximation. Finite element method. Difference schemes for non-stationary problems. Economical difference schemes for multidimensional problems.

Samarskiy A.A., Gulin A.V. Chislennyie metodyi matematicheskoy fiziki. Alyans, 2016 Golubeva K. M., Denisov S. V., Kashpur O. F., Klyushin D. A., Rizhenko A. I. ChiselnI metodi Integruvannya. K., «Lyudmila», 2019. M.M.Moskalkov, A.I.Rizhenko, S.O.Voytsehovskiy ta In. Praktikum z metodIv obchislen. K., MAUP. 2008. BurkIvska V.L., VoytsehIvskiy S.O., Rizhenko A.I. ta In. Metodi obchislen. KiYiv, Vischa shk. 1998. N.S. Bahvalov, A.A Kornev, E.V. Chizhonkov. Chislennyie metodyi. Resheniya zadach i uprazhneniya. Binom, 2016. Bahvalov N.S., Zhidkov N.P., Kobelkov G.N. Chislennyie metodyi. BINOM, 2011. Makarov V.L., Gavrilyuk I.P. Metodi obchislen, t.2,KiYiv,Vischa shkola,1995. Kalitkin, N.N., Alshina E.A., Koryakin P.V. Chislennyie metodyi. Metodyi matematicheskoy fiziki. ITs «Akademiya», 2013. Marchuk G.I. Metodyi vyichislitelnoy matematiki. M. Lan, 2009. A. Iserles. A first course in the numerical analysis of differential equations., Cambridge University Press, 2009. ...

Lectures, independent work, laboratory works, recommended literature processing, doing homework.

Intermediate assessment: The maximal number of available points is 60. 1. Test work : RN 1.1,RN 1.2, RN 1.3,RN 1.4 - 20/12 points. 2. Laboratory work № 1: RN 1.1, RN 3.1, RN 3.2, RN 4.1, RN 4.2 - 10/6 points. 3.La boratory work № 2 : RN 1.1, RN 2.2, RN 3.1, RN 3.2, RN 4.1, RN 4.2 - 8/5 points. 4. Laboratory work № 3 : RN 1.3, RN 2.3, RN 3.1, RN 3.2, RN 4.1, RN 4.2 - 7/4 points. 5. Laboratory work № 4: RN 1.4, RN 2.4, RN 3.1, RN 3.2, RN 4.1, RN 4.2 - 10/6 points. 6. Assessment of independent work: RN 1.1,RN 1.2,RN 1.3, RN 1.4,RN 2.1,RN 2.2, RN 2.3, RN 2.4,RN 4.1, RN 4.2 5/3 points. Final assessment (in the form of exam): The maximal number of available points is 40. The results of study to be assessed are RN 1.1, RN 1.2, RN 1.3, RN 1.4, RN 2.1, RN 2.2, RN 2.3, RN 2.4. The form of exam: writing. The types of assignments are 4 writing assignments (1 theoretical and 3 practical).

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