Head of the Research Group: Prof. Mihály KOVÁCS
Members of the Research Group: Loránd Csongor LACZKÓ, Gyula MOLNÁR
Contact: kovacs.mihaly@itk.ppke.hu
The mathematical models of many time- and space-dependent processes are described by partial differential equations. If there is uncertainty in the equation, then the uncertainty can be modeled using stochastic partial differential equations. If a process taking place in a given location and/or at a given time instance is also affected by events further away in space and/or time, then the process can be described using non-local differential equations.
The focus of the group’s work is the mathematical theory and numerical analysis of the above equations. Recent research topics include the application of stochastic partial differential equations to generate Gaussian random fields on metric graphs, to provide input for various statistical models. The solution of these models requires finite element solutions of elliptic problems on metric graphs, which become large as the size of the net-work grows. To speed up the solution and reduce memory requirements, one may employ domain decomposition methods; this is also one of the group’s current research areas. To speed up computations, we also employ reinforcement learning for adaptive step-size selection in iterative PDE solvers.
The asymptotic behavior of stochastic Hamiltonian particle transport can be characterized by a stochastic differential equation defined on a metric graph.
Future research directions, collaboration opportunities
The research group can assist with the numerical solution of models described by various differential equations. These models can be deterministic or even stochastic, in order to account for the uncertainties inherent in the underlying processes.
Key publications
- Kovács, M., Vághy, M. (2025). Neumann-Neumann type domain decomposition of elliptic problems on metric graphs. BIT NUMERICAL MATHEMATICS 65: (2) 25.
- Pereira, M., Kulcsár, B., Lipták, Gy., Kovács, M., Szederkényi, G. (2024). The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling. TRANSPORTATION RESEARCH PART C: EMERGING TECHNOLOGIES, 158: 13.
- Bolin, D., Kovács, M., Kumar, V., Simas, A. B. (2024). Regularity and numerical approximation of fractional elliptic differential equations on compact metric graphs. MATHEMATICS OF COMPUTATION, 93: (349) PP. 2439–2472.
