1.       

Name of discipline

Numerical method

2.       

Training course

4

3.       

Semester of study

8

4.       

Number of credits

3

5.       

Full name of lecturer

doctor of physical and mathematical Sciences, associate Professor Vasily Volkov

6.       

Objectives of the discipline

– study of the principles of construction and software implementation of numerical algorithms of linear algebra;

– – study of iterative methods for solving nonlinear equations and systems;

– acquisition of skills to choose adequate numerical methods for solving a specific problem;

– study of methods for estimating the correctness of numerical results and error of the solution;

– study of applied aspects of numerical methods of linear algebra.

 introduction to numerical methods implemented in simulation software.

7.       

Prerequisites

– algebra and number theory;

– functional analysis;

– programming method;

– computer mathematics systems

8.       

Content of the discipline

Computer arithmetic. Computational error. Norms of vectors and matrices.

Function approximation methods, numerical differentiation and integration.

Numerical methods for solving systems of LAU. Direct and iterative methods. Error estimate for solving systems of LAU. Condition number.

Calculation of eigenvalues and eigenvectors of matrices. Similarity transformations. The concept of QR algorithm.

Solution of nonlinear equations and systems.

A simple iteration method and Newton’s method. Methods of nonlinear optimization.  Gradient method.

Numerical methods for solving the Cauchy problem for ordinary differential equations.

Numerical methods for solving boundary value problems for ordinary differential equations.

Numerical solution of Fredholm integral equations.

Construction and study of difference schemes for mathematical physics problems.

9.       

Recommended reading

1. Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M. Numerical methods.  M. : BINOM. Lab. knowledge, 2003. 636 p.

2. Samarskiy A. A., Gulin A.V. Numerical methods. M.: Science, 1989. 432 p.

3. Krylov V. I., Bobkov V. V., Monastic P. I. The beginning of the theory of computational methods. Linear algebra and nonlinear equations. Minsk: Science and technology, 1985. 279 p.

4. Fadeev D. K., Fadeeva V. N. Computational methods of linear algebra. SPT. 2002.

5. Voevodin V. V., Kuznetsov Yu. a. Matrices and calculations. M., Science, 1984. 320 p.

6. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P.. Numerical Recipes: the art of scientific computing. New York. 1997. 973p 

7. Numerical methods in 2 parts. Part I. / V. M. Volkov. – Minsk: BSU, 2016.

10.   

Teaching method

passive, active, interactive, verbal, visual, problem

11.   

Language of instruction

Russian

12.   

Conditions (requirements), current control

– laboratory work report;

– test;

13.   

Current certification form

exam