Related papers: Issues with Positivity-Preserving Patankar-type Sc…
Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the…
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 producing unconditionally positive and conservative…
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 methods. This poses a major challenge for…
Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for production-destruction systems. For such schemes, a classical stability analysis does not…
Many natural processes, such as chemical reactions and wave dynamics, are modeled as production-destruction (PD) systems that obey positivity and linear conservation laws. Classical time integrators do not guarantee positivity and can…
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 the solution lacks physical relevance and has a not…
In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is often preferred. On the other…
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 production-destruction system irrespectively of the time…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
In this study, a family of second order process based modified Patankar Runge-Kutta schemes is proposed with both the mass and mole maintained in balance while preserving the positivity of density and pressure with the time step determined…
The first-order linear positivity preserving schemes in time are available for the time dependent Poisson-Nernst-Planck (PNP) equations, second-order linear ones are still challenging. In this paper, we propose the first- and second-order…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
The Poisson-Nernst-Planck (PNP) system is a widely accepted model for simulation of ionic channels. In this paper, we design, analyze, and numerically validate a second order unconditional positivity-preserving scheme for solving a reduced…
Patankar schemes have attracted increasing interest in recent years because they preserve the positivity of the analytical solution of a production-destruction system (PDS) irrespective of the chosen time step size. Although they are now of…
Modified Patankar-Runge-Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production-destruction systems. They adapt explicit Runge-Kutta schemes to ensure positivity and conservation irrespective of…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
Production-destruction systems (PDS) of ordinary differential equations (ODEs) are used to describe physical and biological reactions in nature. The considered quantities are subject to natural laws. Therefore, they preserve positivity and…
We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…