5 papers
Using Machine Learning to Enhance Hyperparameter Optimization in Pandemic Modeling: Case study of COVID-19 Dynamics in Ghana
Thomas Izgin, Andreas Meister, Isaac Azure
In this study, five distinct COVID-19 models developed in different countries, each designed to reflect the prevailing epidemiological condition at the time of formulation, are exa…
A Positivity-Preserving Relaxation Algorithm
Thomas Izgin, Hendrik Ranocha, Chi-Wang Shu
We combine Patankar-type methods with suitable relaxation procedures that are capable of ensuring correct dissipation or conservation of functionals such as entropy or energy while…
Flux-Balanced Patankar-type Schemes for the Compressible Euler Equations
Thomas Izgin, Andreas Meister, Chi-Wang Shu +1
Positivity preservation of key physical quantities in the context of fluid flows, such as density and internal energy, is an essential property of a numerical scheme as otherwise t…
The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
Janina Bender, Thomas Izgin, Philipp Ãffner +1
For hyperbolic conservation laws, the famous Lax-Wendroff theorem delivers sufficient conditions for the limit of a convergent numerical method to be a weak (entropy) solution. Thi…
A Unifying Theory for Runge-Kutta-like Time Integrators: Convergence and Stability
Thomas Izgin
The work deals with two major topics concerning the numerical analysis of Runge-Kutta-like (RK-like) methods, namely their stability and order of convergence. RK-like methods diffe…