UFPFA06 Numerical methods II

Faculty of Philosophy and Science in Opava
Summer 2021
Extent and Intensity
3/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Schee, Ph.D. (lecturer)
doc. RNDr. Jan Schee, Ph.D. (seminar tutor)
Guaranteed by
prof. Ing. Peter Lichard, DrSc.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
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
The aim of the course is to acquaint students with the numerical methods used in physics calculations as well as in the processing of experimental and observational data. Acquired knowledge is exercised by individual solving the problems on the computer, which includes the use of existing program libraries in more complex cases.
Syllabus
  • Monte Carlo method. Random numbers. Pseudorandom number generator with uniform and Gaussian distribution. Multidimensional integrals with general integration areas. Accelerating convergence, importance sampling. Estimation of the statistical error of 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 the n-th order. Euler's method. Modified and improved Euler method. General notes about one-node methods. Local and accumulated error. Directional function and its construction by Taylor's method. Runge-Kutta methods. Examples of methods of the first, second, and third degree. Generalization to the set of the first-order equations. Mesh method. Boundary value problems for ordinary differential equations. Solving mesh equations by Gauss method. Boundary value problem for elliptical partial differential equations in a rectangular area.
    Minimizing functions. Formulation of the problem, global and local minima. One-dimensional problem, variable step method, Rosenbrock method. Multidimensional problem. Random search method, variation of a single parameter, the simplex method, gradient method, simulated annealing.
Literature
    recommended literature
  • Přikryl, P. Numerické metody matematické analýzy. SNTL, 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
Teaching methods
Students' self-study
Lectures, tutorial sessions, regularly assigned and evaluated home tasks.
Assessment methods
Credit
Active participation on tutorial sessions and the timely completion of home tasks is required. Detailed criteria will be announced by the tutorial lecturer. The exam consists of the main written part and a supplemental oral part.
Language of instruction
English
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The attending of lectures is recommended, that of tutorial sessions is compulsory. If a student was absent for serious reasons, the teacher may prescribe him/her an alternative way of fulfilling the duties.
The course is also listed under the following terms Summer 2019, Summer 2020.
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