Issues with positivity-preserving Patankar-type schemes

  title={Issues with positivity-preserving Patankar-type schemes},
  author={Davide Torlo and Philipp {\"O}ffner and Hendrik Ranocha},
  journal={Applied Numerical Mathematics},

On the Stability of Modified Patankar Methods

. Patankar schemes have attracted more and more interests as a time-integration method in the last years due to their unconditionally positivity preserving property. Even though they have been become

An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations



Test Set for Initial Value Problem Solvers

The Bari test set for IVP solvers presents a collection of Initial Value Problems to test solvers for implicit dierential equations to cross the bridge between the application eld and numerical mathematics, by helping people working in several branches of scientic disciplines in choosing the code most suitable for their problems.

A Third-Order Unconditionally Positivity-Preserving Scheme for Production–Destruction Equations with Applications to Non-equilibrium Flows

A third-order unconditionally positivity-preserving modified Patankar Runge–Kutta method for production–destruction equations that is generalized to solve a class of ODEs arising from semi-discrete schemes for PDEs and coupled with the positivity and finite difference weighted essentially non-oscillatory schemes for non-equilibrium flows.

Unconditionally positive and conservative third order modified Patankar–Runge–Kutta discretizations of production–destruction systems

The necessary and sufficient conditions for third order MPRK schemes are derived and the first family of such schemes are introduced, which are based on modified Patankar–Runge–Kutta schemes.

On Order Conditions for modified Patankar-Runge-Kutta schemes

On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes

Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class of general linear

On Lyapunov Stability of Positive and Conservative Time Integrators and Application to Second Order Modified Patankar-Runge-Kutta Schemes

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 the

Recent Developments in the Field of Modified Patankar‐Runge‐Kutta‐methods

This work introduces a strategy to analyze the MPRK22(α)‐schemes in the case of positive and conservative PDS and points out that a usual stability analysis based on Dahlquist's equation is not possible in order to understand the properties of this class of schemes.

Entropy stabilization and property-preserving limiters for ℙ1 discontinuous Galerkin discretizations of scalar hyperbolic problems

The methodology proposed in this paper bridges the gap between entropy stable and positivity-preserving discontinuous Galerkin (DG) methods for nonlinear hyperbolic problems using flux limiters based on entropy conditions and discrete maximum principles.