In this paper, we propose and analyze a positivity-preserving, energy stable numerical
scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with …

Many important applications are modelled by differential equations with positive solutions.
However, it remains an outstanding open problem to develop numerical methods that are …

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 …

In this paper, we develop a fully conservative, positivity-preserving, and entropy-bounded
discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting …

In this paper, we construct a family of modified Patankar Runge–Kutta methods, which is
conservative and unconditionally positivity-preserving, for production–destruction equations …

Abstract Modified Patankar–Runge–Kutta (MPRK) schemes are numerical methods for the
solution of positive and conservative production–destruction systems. They adapt explicit …

Abstract In [6] the modified Patankar–Euler and modified Patankar–Runge–Kutta schemes
were introduced to solve positive and conservative systems of ordinary differential …

Patankar-type schemes are linearly implicit time integration methods designed to be
unconditionally positivity-preserving. However, there are only little results on their stability or …

We extend the energetic variational approach so it can be applied to a chemical reaction
system with general mass action kinetics. Our approach starts with an energy-dissipation …

The poor treatment (or complete omission) of water vapor transport has been identified as a
major limitation suffered by currently available snowpack models. As vapor and heat fluxes …