@article{BeyerGothMueller2022,
  author    = {Beyer, Jacob and Goth, Florian and M{\"u}ller, Tobias},
  title     = {Better integrators for functional renormalization group calculations},
  series = {The European Physical Journal B},
  volume    = {95},
  journal   = {The European Physical Journal B},
  number    = {7},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/s10051-022-00378-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-325131},
  year      = {2022},
  abstract  = {We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice t-t' Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations.},
  language  = {en}
}
@misc{Proell2013,
  type      = {Master Thesis},
  author    = {Pr{\"o}ll, Sebastian},
  title     = {Stability of Switched Epidemiological Models},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-108573},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {In this thesis it is shown how the spread of infectious diseases can be described via mathematical models that show the dynamic behavior of epidemics. Ordinary differential equations are used for the modeling process. SIR and SIRS models are distinguished, depending on whether a disease confers immunity to individuals after recovery or not. There are characteristic parameters for each disease like the infection rate or the recovery rate. These parameters indicate how aggressive a disease acts and how long it takes for an individual to recover, respectively. In general the parameters are time-varying and depend on population groups. For this reason, models with multiple subgroups are introduced, and switched systems are used to carry out time-variant parameters. When investigating such models, the so called disease-free equilibrium is of interest, where no infectives appear within the population. The question is whether there are conditions, under which this equilibrium is stable. Necessary mathematical tools for the stability analysis are presented. The theory of ordinary differential equations, including Lyapunov stability theory, is fundamental. Moreover, convex and nonsmooth analysis, positive systems and differential inclusions are introduced. With these tools, sufficient conditions are given for the disease-free equilibrium of SIS, SIR and SIRS systems to be asymptotically stable.},
  subject      = {Gew{\"o}hnliche Differentialgleichung},
  language  = {en}
}