On Lyapunov stability of positive and conservative time integrators and application to second order modified Patankar–Runge–Kutta schemes

DOI10.1051/m2an/2022031zbMath1492.65191arXiv2202.01099OpenAlexW4220769286MaRDI QIDQ5086979

Thomas Izgin, Stefan Kopecz, Andreas Meister

Publication date: 8 July 2022

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.01099

zbMATH Keywords

Lyapunov stability analysismodified Patankar-Runge-Kutta schemescenter manifold theorem for mapsproduction-destruction systemsunconditionally positive and conservative schemes

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (6)

On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes ⋮ 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 ⋮ An arbitrary high order and positivity preserving method for the shallow water equations ⋮ Issues with positivity-preserving Patankar-type schemes

Cites Work

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• Unconditionally strong stability preserving extensions of the TR-BDF2 method
• 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
• Positivity and Conservation Properties of Some Integration Schemes for Mass Action Kinetics
• Phosphorus Cycles in Lakes and Rivers: Modeling, Analysis, and Simulation
• On the Inverse of the Sum of Matrices
• A detailed view of filaments and sheets in the warm-hot intergalactic medium

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