Research leader name
János Karátson
The Numerical Analysis and Large Networks Research Group was established in 2012. Its aim was to create a national research unit that would provide a broad theoretical integration of applied mathematics research needed by physics, chemistry, biology and other disciplines. Our main areas of interest are the analysis of differential equations and their numerical solutions, further, the study of large networks, thus the investigation of problems described by continuous and discrete models and their interfaces. Our work focuses on the following points.
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In the area of numerical solutions of nonlinear ordinary and partial differential equations, the focus is on developing efficient new methods and improving existing types, including the construction of reliable methods that preserve the qualitative properties of the original model.
For stationary models, our main areas of interest are preconditioned Krylov and quasi-Newton iterations for finite element discretizations, and for time-dependent problems these are Richardson extrapolation, non-standard time discretizations, operator splitting and the Magnus method.
In the context of numerical environmental modelling, we develop numerical solution methods, among other ones, for phenomena in air pollution dispersion, flow and heat propagation, further, disease spreading models. We also use neural networks in the construction of some numerical methods for differential equations In the field of biological applications, the study of network processes has developed into an important area of research. Our main research focus is on the prediction of network dynamics, which helps to describe the spread of different infections in epidemic models, and on the graph theoretic analysis of the reliability of networks. We also analyse models that take into account spatial spread or time delay in epidemic propagation problems. In biological applications, we also deal with the modelling and analysis of immunochemical reactions using systems of nonlinear differential equations.
