Stochastic and statistical modelling (basic research):
Multidimensional and multi-epochal models, Regression models, Insensitivity domains for 1st and 2nd order parameters, Design of experiment, Data analysis methods, Theory of decision making.
Stochastic and statistical modelling (applied and interdisciplinary research):
Safety and integrity of Global Navigation Satellite Systems, Localization of mobile objects in the rail network, Statistical modelling of renewable energy sources, Environmental modelling and weather prediction models, Statistical model for evaluation of wind direction distribution, Applications of regression models in veterinary, Transformation of geodetic networks with different accuracies, Mathematical models for determining of the change-point, Estimates of the critical micelle concentration.
Nonlinear modelling and numerical optimization methods:
Heuristic optimization methods and evolutionary and immunity algorithms, Optimization of power transmission network, Forecasting of dynamic thermal rating of transmission lines, Coordination of renewable and nonrenewable power sources and other optimization task in electroenergetics
Numerical Solution of Integral Equations of the second kind
Degenerate kernel, colocation, Nyström and product integration methods for solution of integral equations of the second kind, especially with singular kernel functions. Aplication of integral equations in physics for example in the solution of induction heating
Numerical solution of ordinary and partial differential equations
Explicit and implicit methods for solution of ODE (Runge kutta methods), finite element method, finite difference method, finite volume method methods for solution of PDEs.
