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

DOI10.1137/22M1480318zbMath1506.65098arXiv2202.11649OpenAlexW4309325534MaRDI QIDQ5058131

Stefan Kopecz, Andreas Meister, Thomas Izgin

Publication date: 2 December 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.11649

zbMATH Keywords

stability analysislinear invariantsnonhyperbolic fixed pointsmodified Patankar-Runge-Kutta schemescenter manifold theorem for mapsproduction-destruction systemsunconditionally positive and conservative schemes

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (3)

On the stability of strong-stability-preserving modified Patankar–Runge–Kutta schemes ⋮ A study of the local dynamics of modified Patankar DeC and higher order modified Patankar–RK methods ⋮ On the dynamics of first and second order GeCo and gBBKS schemes

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems
• Analysis and control of nonlinear systems. A flatness-based approach
• Applications of centre manifold theory
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• A high-order conservative Patankar-type discretisation for stiff systems of production--destruction equations
• On order conditions for modified Patankar-Runge-Kutta schemes
• Unconditionally positive and conservative third order modified Patankar-Runge-Kutta discretizations of production-destruction systems
• Arbitrary high-order, conservative and positivity preserving Patankar-type deferred correction schemes
• \textit{GeCo}: geometric conservative nonstandard schemes for biochemical systems
• Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows
• Qualitative property preservation of high-order operator splitting for the SIR model
• Positivity-preserving adaptive Runge-Kutta methods
• A comprehensive theory on generalized BBKS schemes
• Extension of modified Patankar-Runge-Kutta schemes to nonautonomous production-destruction systems based on Oliver's approach
• A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows
• On the existence of three-stage third-order modified Patankar-Runge-Kutta schemes
• An improved and generalized second order, unconditionally positive, mass conserving integration scheme for biochemical systems
• Phosphorus Cycles in Lakes and Rivers: Modeling, Analysis, and Simulation
• The vectorization of ITPACK 2C
• Conservation de la positivité lors de la discrétisation des problèmes d'évolution paraboliques
• A detailed view of filaments and sheets in the warm-hot intergalactic medium
• Positivity-preserving methods for ordinary differential equations
• On Lyapunov stability of positive and conservative time integrators and application to second order modified Patankar–Runge–Kutta schemes
• Solving Ordinary Differential Equations II
• A special stability problem for linear multistep methods
• Encyclopedia of Complexity and Systems Science

This page was built for publication: On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes