Course: Numerical Methods II

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Course title Numerical Methods II
Course code UF/TF519
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • LICHARD Peter, prof. Ing. DrSc.
Course content
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.

Learning activities and teaching methods
Students' self-study, Lectures, tutorial sessions, regularly assigned and evaluated home tasks.
Recommended literature
  • Marčuk, G.I. - Přikryl, P. - Segeth, K. Metody numerické matematiky. Academia, 1987.
  • Nekvinda, M. - Šrubař, J. - Vild, J. Úvod to numerické matematiky. SNTL, 1976.
  • Přikryl, P. Numerické metody matematické analýzy. SNTL, 1988.
  • Ralston, A. Základy numerické matematiky. Academia, 1978.
  • Riečanová, Z. Numerické metódy a matematická štatistika. SNTL, 1987.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Philosophy and Science in Opava Theoretical Physics (2) Physics courses - Summer