3 citations · 6 across the 12 of their papers we have counts for
14 papers
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 Öffner +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 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…
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…
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters
Thomas Izgin, Stefan Kopecz, Andreas Meister +1
Recently, a stability theory has been developed to study the linear stability of modified Patankar--Runge--Kutta (MPRK) schemes. This stability theory provides sufficient condition…
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…
On the Dynamics of First and Second Order GeCo and gBBKS Schemes
Thomas Izgin, Stefan Kopecz, Angela Martiradonna +1
In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well…
A necessary condition for non oscillatory and positivity preserving time-integration schemes
Thomas Izgin, Philipp Öffner, Davide Torlo
Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for production-destruction systems.…
A Stability Analysis of Modified Patankar-Runge-Kutta methods for a nonlinear Production-Destruction System
Thomas Izgin, Stefan Kopecz, Andreas Meister
Modified Patankar-Runge-Kutta (MPRK) methods preserve the positivity as well as conservativity of a production-destruction system (PDS) of ordinary differential equations for all t…
A study of the local dynamics of modified Patankar DeC and higher order modified Patankar RK methods
Thomas Izgin, Philipp Öffner
Patankar schemes have attracted increasing interest in recent years because they preserve the positivity of the analytical solution of a production-destruction system (PDS) irrespe…
On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes
Juntao Huang, Thomas Izgin, Stefan Kopecz +2
In this paper, we perform stability analysis for a class of second and third order accurate strong-stability-preserving modified Patankar Runge-Kutta (SSPMPRK) schemes, which were…
On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes
Thomas Izgin, Stefan Kopecz, Andreas Meister
Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class o…
On Lyapunov Stability of Positive and Conservative Time Integrators and Application to Second Order Modified Patankar--Runge--Kutta Schemes
Thomas Izgin, Stefan Kopecz, Andreas Meister
Since almost twenty years, modified Patankar--Runge--Kutta (MPRK) methods have proven to be efficient and robust numerical schemes that preserve positivity and conservativity of th…