A Farkas Miklós alkalmazott analízis szemináriumot tantárgyként felvevő hallgatók kutatási beszámolói.
10:15-10:35: Lívia Boda: Investigation of different operator splitting methods
10:35-10:55: András Molnár: Adaptive Time-Stepping for Neural Ordinary Differential Equations
10:55-11:15: Teshome Bayleyegn: Absolute stability and convergence analysis for Multiple Richardson Extrapolation
Ivan Dimov: Multidimensional Sensitivity Analysis of Large-scale Mathematical Models
The aim of the talk is to present various approximation Sensitivity Analysis techniques of Large-scale Mathematical Models. A concept of Sensitivity Analysis and complexity in classes of algorithms will be presented. More precisely, randomized Quasi-Monte Carlo and modified Sobol sequences will be analyzed. As a case study the Unified Danish Eulerian model of air pollution transport (UNI-DEM) will be considered. UNI-DEM is carried out to compute more precisely interaction effects of inputs and sensitivity measures. Various Monte Carlo algorithms have been applied for numerical integration of multidimensional integrals to estimate the sensitivity measures. A comparison of their efficiency will be discussed.
Venelin Todorov: High-accuracy numerical methods for parabolic systems in air pollution modeling
We present different approach es for enhancing the accuracy of the second-order finite difference approximations of two dimensional semilinear parabolic systems. These are the fourth-order compact difference scheme and the fourth-order scheme based on Richardson extrapolation. Our interest is concentrated on a system of ten parabolic partial differential equations in air pollution modeling. We analyze numerical experiments to compare the two approaches with respect to accuracy, computational complexity, nonnegativity preserving, etc. The sixth-order approximation based on the fourth order compact difference scheme combined with Richardson extrapolation is also discussed numerically.
(Joint work with Juri Kandilarov, Ivan Dimov and Luben Vulkov.)
We present the existence of resonance and beats in open and forced chemical oscillatory systems using a superimposed sinusoidal modulation on the inflow rates of the reagents. We demonstrate control over the periodicity of the forced oscillations and show that the time period of beats follows the relation known for forced physical oscillators. Based on experimental results and numerical model simulations, we could show that resonance and beats are internal properties of chemical oscillatory systems. A forced open chemical oscillatory system is a counterpart of the forced oscillators known form the classical mechanics (e.g., driven pendulum), in which instead of applying a periodic external driving force, the periodically changing chemical potential drives the open oscillatory systems.
Integrodifference equations are infinite-dimensional dynamical systems in discrete time. They are motivated by theoretical ecology in order to describe the spatial dispersal and temporal evolution of species having non-overlapping generations. In this talk, we review some recent work addressing two aspects concerning their long-term behavior:
(1) Bifurcation theory of periodic equations, which requires a combination of analytical and numerical techniques (joint work with Christian Aarset)
(2) Numerical Dynamics (persistence of dynamical properties under numerical discretization)