Lecturer(s)


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 nth order. Euler's method. Modified and improved Euler method. General notes about onenode methods. Local and accumulated error. Directional function and its construction by Taylor's method. RungeKutta methods. Examples of methods of the first, second, and third degree. Generalization to the set of the firstorder 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. Onedimensional 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' selfstudy, 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.
