6 papers · 1 filter
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…
Order conditions for Runge--Kutta-like methods with solution-dependent coefficients
Thomas Izgin, David I. Ketcheson, Andreas Meister
In recent years, many positivity-preserving schemes for initial value problems have been constructed by modifying a Runge--Kutta (RK) method by weighting the right-hand side of the…
A Boot-Strapping Technique to Design Dense Output Formulae for Modified Patankar-Runge-Kutta Methods
Thomas Izgin
In this work modified Patankar-Runge-Kutta (MPRK) schemes up to order four are considered and equipped with a dense output formula of appropriate accuracy. Since these time integra…