FPF:UFTF519 Numerical Methods II

UFTF519 Numerical Methods II

Faculty of Philosophy and Science in Opava
Summer 2014

Extent and Intensity

3/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

Guaranteed by

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

Course objectives

To prepare students for effective and correct numerical solution of physical problems and learn how to use computers for numerical calculations.

Syllabus

Monte Carlo method. Random numbers. Random number generator with uniform and Gaussian distribution. Multidimensional integrals with general integration areas. Accelerating convergence importance sampling. Estimation of statistical errors result. Modeling of physical processes using Monte Carlo.
Numerical solution of ordinary differential equations. Cauchy problem for a system of first order equations and the equation of n-th order. Euler's method. Modified and improved Euler method. General knowledge of single-knot methods. Local and accumulated error. Directional function and its structure Taylor method. Runge and Kutta. Examples of methods 1, 2, and third degree. Generalization of the first set of equations Regulations.
Method networks. Boundary value problems for ordinary differential equations. Network solutions by Gauss method. Boundary value problems for partial differential equations of elliptic type in a rectangular area.
Minimizing functions. Formulation of the problem, global and local minimum. One-dimensional problem, the method of variable step Rosenbrock method. Multivariate role. Random search method, method of variation of one parameter, the simplex method, gradient method, simulated annealing.

Literature

recommended literature

Přikryl, P. Numerické metody matematické analýzy. SNTL, 1988. info
Segethová, J. Základy numerické matematiky. Karolinum, 1988. info
Marčuk, G.I. - Přikryl, P. - Segeth, K. Metody numerické matematiky. Academia, 1987. info
Riečanová, Z. Numerické metódy a matematická štatistika. SNTL, 1987. info
Ralston, A. Základy numerické matematiky. Academia, 1978. info
Nekvinda, M. - Šrubař, J. - Vild, J. Úvod to numerické matematiky. SNTL, 1976. info

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.

Teacher's information

* 60% attendance in seminars.